Mixing
Interest involving different years, but same or lower 2nd value?
$begingroup$
When selling your property you receive the following offers :
(a) € 100 000 on 1.1.18 and € 100 000 on 1.1.20
(b) € 150 000 on 1.1.18 and € 50 000 on 1.1.19
Assume interest is 3%
Which offer is better?
Now this is how I believe this should be done.
Is my understanding correct or am i completely off?
a) FV= 100 000(1+0.03*2)=106 000+ 100 000=206 000
b) FV= 150 000(1+0.03*1)=154 000+ 50 000= 204 500
finance
asked Jan 29 at 9:43
Vanessa LaVanessa La
61
$endgroup$
add a comment |
$begingroup$
When selling your property you receive the following offers :
(a) € 100 000 on 1.1.18 and € 100 000 on 1.1.20
(b) € 150 000 on 1.1.18 and € 50 000 on 1.1.19
Assume interest is 3%
Which offer is better?
Now this is how I believe this should be done.
Is my understanding correct or am i completely off?
a) FV= 100 000(1+0.03*2)=106 000+ 100 000=206 000
b) FV= 150 000(1+0.03*1)=154 000+ 50 000= 204 500
finance
asked Jan 29 at 9:43
Vanessa LaVanessa La
61
$endgroup$
2
$begingroup$
It's otherwise ok, but instead of $(1+0.03 times 2)$ I would calculate $(1+0.03)^2$ (compound interest). There is a small difference between the results, and the first one is only an approximation of the latter. Also, pay attention to your notation. You have written $$ 100~000(1+0.03*2)=106~000+ 100~000 $$ which is not true if you evaluate both sides. But I understand what you want to calculate.
$endgroup$
– Matti P.
Jan 29 at 9:48
$begingroup$
It should be intuitively obvious that (b) is the better offer because you get more money on 1.1.18 and the balance sooner than in (a). Your mistake is that you have calculated the value of (a) on 1.1.20 but the value of (b) on 1.1.19, so you cannot compare these amounts.
$endgroup$
– gandalf61
Jan 29 at 12:15
$begingroup$
Vanessa, please clarify if the interest rate is compound or simple.
$endgroup$
– callculus
Jan 29 at 12:40
add a comment |
$begingroup$
When selling your property you receive the following offers :
(a) € 100 000 on 1.1.18 and € 100 000 on 1.1.20
(b) € 150 000 on 1.1.18 and € 50 000 on 1.1.19
Assume interest is 3%
Which offer is better?
Now this is how I believe this should be done.
Is my understanding correct or am i completely off?
a) FV= 100 000(1+0.03*2)=106 000+ 100 000=206 000
b) FV= 150 000(1+0.03*1)=154 000+ 50 000= 204 500
finance
asked Jan 29 at 9:43
Vanessa LaVanessa La
61
$endgroup$
When selling your property you receive the following offers :
(a) € 100 000 on 1.1.18 and € 100 000 on 1.1.20
(b) € 150 000 on 1.1.18 and € 50 000 on 1.1.19
Assume interest is 3%
Which offer is better?
Now this is how I believe this should be done.
Is my understanding correct or am i completely off?
a) FV= 100 000(1+0.03*2)=106 000+ 100 000=206 000
b) FV= 150 000(1+0.03*1)=154 000+ 50 000= 204 500
finance
finance
asked Jan 29 at 9:43
Vanessa LaVanessa La
61
asked Jan 29 at 9:43
Vanessa LaVanessa La
61
asked Jan 29 at 9:43
Vanessa LaVanessa La
61
asked Jan 29 at 9:43
Vanessa LaVanessa La
61
asked Jan 29 at 9:43
Vanessa LaVanessa La
61
61
2
$begingroup$
It's otherwise ok, but instead of $(1+0.03 times 2)$ I would calculate $(1+0.03)^2$ (compound interest). There is a small difference between the results, and the first one is only an approximation of the latter. Also, pay attention to your notation. You have written $$ 100~000(1+0.03*2)=106~000+ 100~000 $$ which is not true if you evaluate both sides. But I understand what you want to calculate.
$endgroup$
– Matti P.
Jan 29 at 9:48
$begingroup$
It should be intuitively obvious that (b) is the better offer because you get more money on 1.1.18 and the balance sooner than in (a). Your mistake is that you have calculated the value of (a) on 1.1.20 but the value of (b) on 1.1.19, so you cannot compare these amounts.
$endgroup$
– gandalf61
Jan 29 at 12:15
$begingroup$
Vanessa, please clarify if the interest rate is compound or simple.
$endgroup$
– callculus
Jan 29 at 12:40
add a comment |
2
$begingroup$
It's otherwise ok, but instead of $(1+0.03 times 2)$ I would calculate $(1+0.03)^2$ (compound interest). There is a small difference between the results, and the first one is only an approximation of the latter. Also, pay attention to your notation. You have written $$ 100~000(1+0.03*2)=106~000+ 100~000 $$ which is not true if you evaluate both sides. But I understand what you want to calculate.
$endgroup$
– Matti P.
Jan 29 at 9:48
$begingroup$
It should be intuitively obvious that (b) is the better offer because you get more money on 1.1.18 and the balance sooner than in (a). Your mistake is that you have calculated the value of (a) on 1.1.20 but the value of (b) on 1.1.19, so you cannot compare these amounts.
$endgroup$
– gandalf61
Jan 29 at 12:15
$begingroup$
Vanessa, please clarify if the interest rate is compound or simple.
$endgroup$
– callculus
Jan 29 at 12:40
2
2
$begingroup$
It's otherwise ok, but instead of $(1+0.03 times 2)$ I would calculate $(1+0.03)^2$ (compound interest). There is a small difference between the results, and the first one is only an approximation of the latter. Also, pay attention to your notation. You have written $$ 100~000(1+0.03*2)=106~000+ 100~000 $$ which is not true if you evaluate both sides. But I understand what you want to calculate.
$endgroup$
– Matti P.
Jan 29 at 9:48
$begingroup$
It's otherwise ok, but instead of $(1+0.03 times 2)$ I would calculate $(1+0.03)^2$ (compound interest). There is a small difference between the results, and the first one is only an approximation of the latter. Also, pay attention to your notation. You have written $$ 100~000(1+0.03*2)=106~000+ 100~000 $$ which is not true if you evaluate both sides. But I understand what you want to calculate.
$endgroup$
– Matti P.
Jan 29 at 9:48
$begingroup$
It should be intuitively obvious that (b) is the better offer because you get more money on 1.1.18 and the balance sooner than in (a). Your mistake is that you have calculated the value of (a) on 1.1.20 but the value of (b) on 1.1.19, so you cannot compare these amounts.
$endgroup$
– gandalf61
Jan 29 at 12:15
$begingroup$
It should be intuitively obvious that (b) is the better offer because you get more money on 1.1.18 and the balance sooner than in (a). Your mistake is that you have calculated the value of (a) on 1.1.20 but the value of (b) on 1.1.19, so you cannot compare these amounts.
$endgroup$
– gandalf61
Jan 29 at 12:15
$begingroup$
Vanessa, please clarify if the interest rate is compound or simple.
$endgroup$
– callculus
Jan 29 at 12:40
$begingroup$
Vanessa, please clarify if the interest rate is compound or simple.
$endgroup$
– callculus
Jan 29 at 12:40
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
I think you should not calculate the end value of both payments, as it implies comparing (using your numbers) $$206 000$ at 1.1.2020 to $$204 500$ at 1.1.2019. It's better to compare the net present value of both proposals, which are
$$NPV_1=100 000+frac{100 000}{(1+0.03)^2}=194259.59$$
and
$$NPV_2=150 000+frac{50 000}{(1+0.03)}=198543.69$$
As you can see, it's better to choose the second option. This is not surprising, as the total $$200000$ is received earlier than in the first.
Edit: The net present value is just the value today. That's why we discount future payments, i.e., we divide by $(1+r)^t$. The future value is the value at some point in the future. And this is the reason for capitalization, i.e., multiplying by $(1+r)^t$. In the first case, we want to determine how much is worth today a given payment schedule, while in the second we obtain the value at some point in the future. Both the future value and the present value should give you the same answer provided the future values are obtained for the same (future) date.
For example, if you computed the future value of the schedules in your problem at 1.1.2020, you'd obtain
$$ FV_1=100000(1+0.03)^2+100000=206090$$
$$ FV_1=150000(1+0.03)^2+50000(1+0.03)=210635.$$
This is due to the fact that the future value is just the net present value capitalized. In your case, it is easy to see that
$$ FV_i=NPV_i(1+0.03)^2.$$
answered Jan 29 at 10:10
PatricioPatricio
3427
$endgroup$
$begingroup$
Relating to this present value, how do you differentiate solving for present value or future value?
$endgroup$
– Vanessa La
Jan 29 at 10:49
$begingroup$
The Present value is just the value today. That's why we discount future payments (we divide by $(1+r)^t$). The future value is the value at some point in the future. And this is the reason for capitalization (multiplying by $(1+r)^t$).
$endgroup$
– Patricio
Jan 29 at 13:21
$begingroup$
I've edited the answer to make it clearer.
$endgroup$
– Patricio
Jan 29 at 13:35
add a comment |
$begingroup$
Not quite. The second offer should look better because you receive money earlier
Your error is to calculate the values at the point the last payments are received, but these are different times, making them incomparable. You should choose a particular date for the comparison
If you are measuring the value at 1.1.20 then your calculations should be
$$€100000(1+0.03)^2+€100000 = €206090$$
$$€150000(1+0.03)^2+€50000(1+0.03) = €210635$$If you are measuring the value at 1.1.19 then your calculations should be
$$€100000(1+0.03)+€100000/(1+0.03) approx €200087$$
$$€150000(1+0.03)+€50000 = €204500$$If you are measuring the value at 1.1.18 then your calculations should be
$$€100000+€100000/(1+0.03)^2 approx €194260$$
$$€150000+€50000/(1+0.03) approx €198544 $$
answered Jan 29 at 10:10
HenryHenry
101k482169
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I think you should not calculate the end value of both payments, as it implies comparing (using your numbers) $$206 000$ at 1.1.2020 to $$204 500$ at 1.1.2019. It's better to compare the net present value of both proposals, which are
$$NPV_1=100 000+frac{100 000}{(1+0.03)^2}=194259.59$$
and
$$NPV_2=150 000+frac{50 000}{(1+0.03)}=198543.69$$
As you can see, it's better to choose the second option. This is not surprising, as the total $$200000$ is received earlier than in the first.
Edit: The net present value is just the value today. That's why we discount future payments, i.e., we divide by $(1+r)^t$. The future value is the value at some point in the future. And this is the reason for capitalization, i.e., multiplying by $(1+r)^t$. In the first case, we want to determine how much is worth today a given payment schedule, while in the second we obtain the value at some point in the future. Both the future value and the present value should give you the same answer provided the future values are obtained for the same (future) date.
For example, if you computed the future value of the schedules in your problem at 1.1.2020, you'd obtain
$$ FV_1=100000(1+0.03)^2+100000=206090$$
$$ FV_1=150000(1+0.03)^2+50000(1+0.03)=210635.$$
This is due to the fact that the future value is just the net present value capitalized. In your case, it is easy to see that
$$ FV_i=NPV_i(1+0.03)^2.$$
answered Jan 29 at 10:10
PatricioPatricio
3427
$endgroup$
$begingroup$
Relating to this present value, how do you differentiate solving for present value or future value?
$endgroup$
– Vanessa La
Jan 29 at 10:49
$begingroup$
The Present value is just the value today. That's why we discount future payments (we divide by $(1+r)^t$). The future value is the value at some point in the future. And this is the reason for capitalization (multiplying by $(1+r)^t$).
$endgroup$
– Patricio
Jan 29 at 13:21
$begingroup$
I've edited the answer to make it clearer.
$endgroup$
– Patricio
Jan 29 at 13:35
add a comment |
$begingroup$
I think you should not calculate the end value of both payments, as it implies comparing (using your numbers) $$206 000$ at 1.1.2020 to $$204 500$ at 1.1.2019. It's better to compare the net present value of both proposals, which are
$$NPV_1=100 000+frac{100 000}{(1+0.03)^2}=194259.59$$
and
$$NPV_2=150 000+frac{50 000}{(1+0.03)}=198543.69$$
As you can see, it's better to choose the second option. This is not surprising, as the total $$200000$ is received earlier than in the first.
Edit: The net present value is just the value today. That's why we discount future payments, i.e., we divide by $(1+r)^t$. The future value is the value at some point in the future. And this is the reason for capitalization, i.e., multiplying by $(1+r)^t$. In the first case, we want to determine how much is worth today a given payment schedule, while in the second we obtain the value at some point in the future. Both the future value and the present value should give you the same answer provided the future values are obtained for the same (future) date.
For example, if you computed the future value of the schedules in your problem at 1.1.2020, you'd obtain
$$ FV_1=100000(1+0.03)^2+100000=206090$$
$$ FV_1=150000(1+0.03)^2+50000(1+0.03)=210635.$$
This is due to the fact that the future value is just the net present value capitalized. In your case, it is easy to see that
$$ FV_i=NPV_i(1+0.03)^2.$$
answered Jan 29 at 10:10
PatricioPatricio
3427
$endgroup$
$begingroup$
Relating to this present value, how do you differentiate solving for present value or future value?
$endgroup$
– Vanessa La
Jan 29 at 10:49
$begingroup$
The Present value is just the value today. That's why we discount future payments (we divide by $(1+r)^t$). The future value is the value at some point in the future. And this is the reason for capitalization (multiplying by $(1+r)^t$).
$endgroup$
– Patricio
Jan 29 at 13:21
$begingroup$
I've edited the answer to make it clearer.
$endgroup$
– Patricio
Jan 29 at 13:35
add a comment |
$begingroup$
I think you should not calculate the end value of both payments, as it implies comparing (using your numbers) $$206 000$ at 1.1.2020 to $$204 500$ at 1.1.2019. It's better to compare the net present value of both proposals, which are
$$NPV_1=100 000+frac{100 000}{(1+0.03)^2}=194259.59$$
and
$$NPV_2=150 000+frac{50 000}{(1+0.03)}=198543.69$$
As you can see, it's better to choose the second option. This is not surprising, as the total $$200000$ is received earlier than in the first.
Edit: The net present value is just the value today. That's why we discount future payments, i.e., we divide by $(1+r)^t$. The future value is the value at some point in the future. And this is the reason for capitalization, i.e., multiplying by $(1+r)^t$. In the first case, we want to determine how much is worth today a given payment schedule, while in the second we obtain the value at some point in the future. Both the future value and the present value should give you the same answer provided the future values are obtained for the same (future) date.
For example, if you computed the future value of the schedules in your problem at 1.1.2020, you'd obtain
$$ FV_1=100000(1+0.03)^2+100000=206090$$
$$ FV_1=150000(1+0.03)^2+50000(1+0.03)=210635.$$
This is due to the fact that the future value is just the net present value capitalized. In your case, it is easy to see that
$$ FV_i=NPV_i(1+0.03)^2.$$
answered Jan 29 at 10:10
PatricioPatricio
3427
$endgroup$
I think you should not calculate the end value of both payments, as it implies comparing (using your numbers) $$206 000$ at 1.1.2020 to $$204 500$ at 1.1.2019. It's better to compare the net present value of both proposals, which are
$$NPV_1=100 000+frac{100 000}{(1+0.03)^2}=194259.59$$
and
$$NPV_2=150 000+frac{50 000}{(1+0.03)}=198543.69$$
As you can see, it's better to choose the second option. This is not surprising, as the total $$200000$ is received earlier than in the first.
Edit: The net present value is just the value today. That's why we discount future payments, i.e., we divide by $(1+r)^t$. The future value is the value at some point in the future. And this is the reason for capitalization, i.e., multiplying by $(1+r)^t$. In the first case, we want to determine how much is worth today a given payment schedule, while in the second we obtain the value at some point in the future. Both the future value and the present value should give you the same answer provided the future values are obtained for the same (future) date.
For example, if you computed the future value of the schedules in your problem at 1.1.2020, you'd obtain
$$ FV_1=100000(1+0.03)^2+100000=206090$$
$$ FV_1=150000(1+0.03)^2+50000(1+0.03)=210635.$$
This is due to the fact that the future value is just the net present value capitalized. In your case, it is easy to see that
$$ FV_i=NPV_i(1+0.03)^2.$$
answered Jan 29 at 10:10
PatricioPatricio
3427
edited Jan 29 at 13:34
answered Jan 29 at 10:10
PatricioPatricio
3427
answered Jan 29 at 10:10
PatricioPatricio
3427
answered Jan 29 at 10:10
PatricioPatricio
3427
3427
$begingroup$
Relating to this present value, how do you differentiate solving for present value or future value?
$endgroup$
– Vanessa La
Jan 29 at 10:49
$begingroup$
The Present value is just the value today. That's why we discount future payments (we divide by $(1+r)^t$). The future value is the value at some point in the future. And this is the reason for capitalization (multiplying by $(1+r)^t$).
$endgroup$
– Patricio
Jan 29 at 13:21
$begingroup$
I've edited the answer to make it clearer.
$endgroup$
– Patricio
Jan 29 at 13:35
add a comment |
$begingroup$
Relating to this present value, how do you differentiate solving for present value or future value?
$endgroup$
– Vanessa La
Jan 29 at 10:49
$begingroup$
The Present value is just the value today. That's why we discount future payments (we divide by $(1+r)^t$). The future value is the value at some point in the future. And this is the reason for capitalization (multiplying by $(1+r)^t$).
$endgroup$
– Patricio
Jan 29 at 13:21
$begingroup$
I've edited the answer to make it clearer.
$endgroup$
– Patricio
Jan 29 at 13:35
$begingroup$
Relating to this present value, how do you differentiate solving for present value or future value?
$endgroup$
– Vanessa La
Jan 29 at 10:49
$begingroup$
Relating to this present value, how do you differentiate solving for present value or future value?
$endgroup$
– Vanessa La
Jan 29 at 10:49
$begingroup$
The Present value is just the value today. That's why we discount future payments (we divide by $(1+r)^t$). The future value is the value at some point in the future. And this is the reason for capitalization (multiplying by $(1+r)^t$).
$endgroup$
– Patricio
Jan 29 at 13:21
$begingroup$
The Present value is just the value today. That's why we discount future payments (we divide by $(1+r)^t$). The future value is the value at some point in the future. And this is the reason for capitalization (multiplying by $(1+r)^t$).
$endgroup$
– Patricio
Jan 29 at 13:21
$begingroup$
I've edited the answer to make it clearer.
$endgroup$
– Patricio
Jan 29 at 13:35
$begingroup$
I've edited the answer to make it clearer.
$endgroup$
– Patricio
Jan 29 at 13:35
add a comment |
$begingroup$
Not quite. The second offer should look better because you receive money earlier
Your error is to calculate the values at the point the last payments are received, but these are different times, making them incomparable. You should choose a particular date for the comparison
If you are measuring the value at 1.1.20 then your calculations should be
$$€100000(1+0.03)^2+€100000 = €206090$$
$$€150000(1+0.03)^2+€50000(1+0.03) = €210635$$If you are measuring the value at 1.1.19 then your calculations should be
$$€100000(1+0.03)+€100000/(1+0.03) approx €200087$$
$$€150000(1+0.03)+€50000 = €204500$$If you are measuring the value at 1.1.18 then your calculations should be
$$€100000+€100000/(1+0.03)^2 approx €194260$$
$$€150000+€50000/(1+0.03) approx €198544 $$
answered Jan 29 at 10:10
HenryHenry
101k482169
$endgroup$
add a comment |
$begingroup$
Not quite. The second offer should look better because you receive money earlier
Your error is to calculate the values at the point the last payments are received, but these are different times, making them incomparable. You should choose a particular date for the comparison
If you are measuring the value at 1.1.20 then your calculations should be
$$€100000(1+0.03)^2+€100000 = €206090$$
$$€150000(1+0.03)^2+€50000(1+0.03) = €210635$$If you are measuring the value at 1.1.19 then your calculations should be
$$€100000(1+0.03)+€100000/(1+0.03) approx €200087$$
$$€150000(1+0.03)+€50000 = €204500$$If you are measuring the value at 1.1.18 then your calculations should be
$$€100000+€100000/(1+0.03)^2 approx €194260$$
$$€150000+€50000/(1+0.03) approx €198544 $$
answered Jan 29 at 10:10
HenryHenry
101k482169
$endgroup$
add a comment |
$begingroup$
Not quite. The second offer should look better because you receive money earlier
Your error is to calculate the values at the point the last payments are received, but these are different times, making them incomparable. You should choose a particular date for the comparison
If you are measuring the value at 1.1.20 then your calculations should be
$$€100000(1+0.03)^2+€100000 = €206090$$
$$€150000(1+0.03)^2+€50000(1+0.03) = €210635$$If you are measuring the value at 1.1.19 then your calculations should be
$$€100000(1+0.03)+€100000/(1+0.03) approx €200087$$
$$€150000(1+0.03)+€50000 = €204500$$If you are measuring the value at 1.1.18 then your calculations should be
$$€100000+€100000/(1+0.03)^2 approx €194260$$
$$€150000+€50000/(1+0.03) approx €198544 $$
answered Jan 29 at 10:10
HenryHenry
101k482169
$endgroup$
Not quite. The second offer should look better because you receive money earlier
Your error is to calculate the values at the point the last payments are received, but these are different times, making them incomparable. You should choose a particular date for the comparison
If you are measuring the value at 1.1.20 then your calculations should be
$$€100000(1+0.03)^2+€100000 = €206090$$
$$€150000(1+0.03)^2+€50000(1+0.03) = €210635$$If you are measuring the value at 1.1.19 then your calculations should be
$$€100000(1+0.03)+€100000/(1+0.03) approx €200087$$
$$€150000(1+0.03)+€50000 = €204500$$If you are measuring the value at 1.1.18 then your calculations should be
$$€100000+€100000/(1+0.03)^2 approx €194260$$
$$€150000+€50000/(1+0.03) approx €198544 $$
answered Jan 29 at 10:10
HenryHenry
101k482169
answered Jan 29 at 10:10
HenryHenry
101k482169
answered Jan 29 at 10:10
HenryHenry
101k482169
answered Jan 29 at 10:10
HenryHenry
101k482169
101k482169
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2
$begingroup$
It's otherwise ok, but instead of $(1+0.03 times 2)$ I would calculate $(1+0.03)^2$ (compound interest). There is a small difference between the results, and the first one is only an approximation of the latter. Also, pay attention to your notation. You have written $$ 100~000(1+0.03*2)=106~000+ 100~000 $$ which is not true if you evaluate both sides. But I understand what you want to calculate.
$endgroup$
– Matti P.
Jan 29 at 9:48
$begingroup$
It should be intuitively obvious that (b) is the better offer because you get more money on 1.1.18 and the balance sooner than in (a). Your mistake is that you have calculated the value of (a) on 1.1.20 but the value of (b) on 1.1.19, so you cannot compare these amounts.
$endgroup$
– gandalf61
Jan 29 at 12:15
$begingroup$
Vanessa, please clarify if the interest rate is compound or simple.
$endgroup$
– callculus
Jan 29 at 12:40