Mixing
Final Payment Value Compound Interest Question
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A demand loan of $$4000.00$ is repaid by payments of $$2000.00$ after two years, $$2000.00$ after four years, and a final payment after six years.
Interest is $6%$ compounded quarterly for the first two years, $7%$ compounded annually for the next two years, and 7% compounded semi-annually thereafter. What is the size of the final payment?
I know how to make all these precursor calculations but I'm very lost on which formula to use to find the final amount.
payment. $3000(1+0.0175)^{0.5}$
Payment $3000(1+0.04)^{2}$
algebra-precalculus finance
edited 10 hours ago
NoChance
3,58121221
asked 10 hours ago
John Deer
111
New contributor
John Deer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
|
show 3 more comments
up vote
1
down vote
favorite
A demand loan of $$4000.00$ is repaid by payments of $$2000.00$ after two years, $$2000.00$ after four years, and a final payment after six years.
Interest is $6%$ compounded quarterly for the first two years, $7%$ compounded annually for the next two years, and 7% compounded semi-annually thereafter. What is the size of the final payment?
I know how to make all these precursor calculations but I'm very lost on which formula to use to find the final amount.
payment. $3000(1+0.0175)^{0.5}$
Payment $3000(1+0.04)^{2}$
algebra-precalculus finance
edited 10 hours ago
NoChance
3,58121221
asked 10 hours ago
John Deer
111
New contributor
John Deer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
Far better to use understanding than to use a formula.
– Gerry Myerson
10 hours ago
I get that but I'm struggling with the concept and I think knowing the formula would allow me the context to mentally frame it better.
– John Deer
10 hours ago
I think understanding the mathematics would be a better idea, but each to his/her own.
– Gerry Myerson
10 hours ago
If you would like to try and give me a better understanding I would very much like to hear it.
– John Deer
10 hours ago
1
OK. What's the balance after two years, before the first repayment? What's the balance after two years, after the first reapyment? Same question for after 4 years, before and after the second repayment. Then, what's the balance at the end of six years?
– Gerry Myerson
10 hours ago
|
show 3 more comments
up vote
1
down vote
favorite
up vote
1
down vote
favorite
A demand loan of $$4000.00$ is repaid by payments of $$2000.00$ after two years, $$2000.00$ after four years, and a final payment after six years.
Interest is $6%$ compounded quarterly for the first two years, $7%$ compounded annually for the next two years, and 7% compounded semi-annually thereafter. What is the size of the final payment?
I know how to make all these precursor calculations but I'm very lost on which formula to use to find the final amount.
payment. $3000(1+0.0175)^{0.5}$
Payment $3000(1+0.04)^{2}$
algebra-precalculus finance
edited 10 hours ago
NoChance
3,58121221
asked 10 hours ago
John Deer
111
New contributor
John Deer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
A demand loan of $$4000.00$ is repaid by payments of $$2000.00$ after two years, $$2000.00$ after four years, and a final payment after six years.
Interest is $6%$ compounded quarterly for the first two years, $7%$ compounded annually for the next two years, and 7% compounded semi-annually thereafter. What is the size of the final payment?
I know how to make all these precursor calculations but I'm very lost on which formula to use to find the final amount.
payment. $3000(1+0.0175)^{0.5}$
Payment $3000(1+0.04)^{2}$
algebra-precalculus finance
algebra-precalculus finance
edited 10 hours ago
NoChance
3,58121221
asked 10 hours ago
John Deer
111
New contributor
John Deer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 10 hours ago
NoChance
3,58121221
asked 10 hours ago
John Deer
111
New contributor
John Deer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 10 hours ago
NoChance
3,58121221
edited 10 hours ago
NoChance
3,58121221
edited 10 hours ago
NoChance
3,58121221
3,58121221
asked 10 hours ago
John Deer
111
New contributor
John Deer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 10 hours ago
John Deer
111
asked 10 hours ago
John Deer
111
111
New contributor
John Deer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
John Deer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
John Deer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
Far better to use understanding than to use a formula.
– Gerry Myerson
10 hours ago
I get that but I'm struggling with the concept and I think knowing the formula would allow me the context to mentally frame it better.
– John Deer
10 hours ago
I think understanding the mathematics would be a better idea, but each to his/her own.
– Gerry Myerson
10 hours ago
If you would like to try and give me a better understanding I would very much like to hear it.
– John Deer
10 hours ago
1
OK. What's the balance after two years, before the first repayment? What's the balance after two years, after the first reapyment? Same question for after 4 years, before and after the second repayment. Then, what's the balance at the end of six years?
– Gerry Myerson
10 hours ago
|
show 3 more comments
1
Far better to use understanding than to use a formula.
– Gerry Myerson
10 hours ago
I get that but I'm struggling with the concept and I think knowing the formula would allow me the context to mentally frame it better.
– John Deer
10 hours ago
I think understanding the mathematics would be a better idea, but each to his/her own.
– Gerry Myerson
10 hours ago
If you would like to try and give me a better understanding I would very much like to hear it.
– John Deer
10 hours ago
1
OK. What's the balance after two years, before the first repayment? What's the balance after two years, after the first reapyment? Same question for after 4 years, before and after the second repayment. Then, what's the balance at the end of six years?
– Gerry Myerson
10 hours ago
1
1
Far better to use understanding than to use a formula.
– Gerry Myerson
10 hours ago
Far better to use understanding than to use a formula.
– Gerry Myerson
10 hours ago
I get that but I'm struggling with the concept and I think knowing the formula would allow me the context to mentally frame it better.
– John Deer
10 hours ago
I get that but I'm struggling with the concept and I think knowing the formula would allow me the context to mentally frame it better.
– John Deer
10 hours ago
I think understanding the mathematics would be a better idea, but each to his/her own.
– Gerry Myerson
10 hours ago
I think understanding the mathematics would be a better idea, but each to his/her own.
– Gerry Myerson
10 hours ago
If you would like to try and give me a better understanding I would very much like to hear it.
– John Deer
10 hours ago
If you would like to try and give me a better understanding I would very much like to hear it.
– John Deer
10 hours ago
1
1
OK. What's the balance after two years, before the first repayment? What's the balance after two years, after the first reapyment? Same question for after 4 years, before and after the second repayment. Then, what's the balance at the end of six years?
– Gerry Myerson
10 hours ago
OK. What's the balance after two years, before the first repayment? What's the balance after two years, after the first reapyment? Same question for after 4 years, before and after the second repayment. Then, what's the balance at the end of six years?
– Gerry Myerson
10 hours ago
|
show 3 more comments
1 Answer
1
active
oldest
votes
up vote
0
down vote
The final payment can be calculated in steps by figuring how much the loan has grown with interest over each time period before each of the stage payments. I'm assuming the interest for each time period is simply the annual rate divided by the number of time periods per year.
$$P_F = ((4000cdot 1.015^8 -2000)1.07^2 - 2000)1.035^4 = $997.30$$
answered 10 hours ago
Phil H
3,8282312
I'm confused where you're getting your N value as I thought it was numbers of years divided by interests compounds per year so for the first 2 years wouldn't it be 4000(1.015)^0.5 as it Would be 2 years divided by 4 (quarterly interest compounds)
– John Deer
10 hours ago
No, it's 1.015 to the power of the number of quarters in 2 years which is 8.Then 1.07 to the power of the number of years which is 2 and finally 1.035 to the power of the number of half years in 2 years which is 4.
– Phil H
8 hours ago
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
The final payment can be calculated in steps by figuring how much the loan has grown with interest over each time period before each of the stage payments. I'm assuming the interest for each time period is simply the annual rate divided by the number of time periods per year.
$$P_F = ((4000cdot 1.015^8 -2000)1.07^2 - 2000)1.035^4 = $997.30$$
answered 10 hours ago
Phil H
3,8282312
I'm confused where you're getting your N value as I thought it was numbers of years divided by interests compounds per year so for the first 2 years wouldn't it be 4000(1.015)^0.5 as it Would be 2 years divided by 4 (quarterly interest compounds)
– John Deer
10 hours ago
No, it's 1.015 to the power of the number of quarters in 2 years which is 8.Then 1.07 to the power of the number of years which is 2 and finally 1.035 to the power of the number of half years in 2 years which is 4.
– Phil H
8 hours ago
add a comment |
up vote
0
down vote
The final payment can be calculated in steps by figuring how much the loan has grown with interest over each time period before each of the stage payments. I'm assuming the interest for each time period is simply the annual rate divided by the number of time periods per year.
$$P_F = ((4000cdot 1.015^8 -2000)1.07^2 - 2000)1.035^4 = $997.30$$
answered 10 hours ago
Phil H
3,8282312
I'm confused where you're getting your N value as I thought it was numbers of years divided by interests compounds per year so for the first 2 years wouldn't it be 4000(1.015)^0.5 as it Would be 2 years divided by 4 (quarterly interest compounds)
– John Deer
10 hours ago
No, it's 1.015 to the power of the number of quarters in 2 years which is 8.Then 1.07 to the power of the number of years which is 2 and finally 1.035 to the power of the number of half years in 2 years which is 4.
– Phil H
8 hours ago
add a comment |
up vote
0
down vote
up vote
0
down vote
The final payment can be calculated in steps by figuring how much the loan has grown with interest over each time period before each of the stage payments. I'm assuming the interest for each time period is simply the annual rate divided by the number of time periods per year.
$$P_F = ((4000cdot 1.015^8 -2000)1.07^2 - 2000)1.035^4 = $997.30$$
answered 10 hours ago
Phil H
3,8282312
The final payment can be calculated in steps by figuring how much the loan has grown with interest over each time period before each of the stage payments. I'm assuming the interest for each time period is simply the annual rate divided by the number of time periods per year.
$$P_F = ((4000cdot 1.015^8 -2000)1.07^2 - 2000)1.035^4 = $997.30$$
answered 10 hours ago
Phil H
3,8282312
answered 10 hours ago
Phil H
3,8282312
answered 10 hours ago
Phil H
3,8282312
answered 10 hours ago
Phil H
3,8282312
3,8282312
I'm confused where you're getting your N value as I thought it was numbers of years divided by interests compounds per year so for the first 2 years wouldn't it be 4000(1.015)^0.5 as it Would be 2 years divided by 4 (quarterly interest compounds)
– John Deer
10 hours ago
No, it's 1.015 to the power of the number of quarters in 2 years which is 8.Then 1.07 to the power of the number of years which is 2 and finally 1.035 to the power of the number of half years in 2 years which is 4.
– Phil H
8 hours ago
add a comment |
I'm confused where you're getting your N value as I thought it was numbers of years divided by interests compounds per year so for the first 2 years wouldn't it be 4000(1.015)^0.5 as it Would be 2 years divided by 4 (quarterly interest compounds)
– John Deer
10 hours ago
No, it's 1.015 to the power of the number of quarters in 2 years which is 8.Then 1.07 to the power of the number of years which is 2 and finally 1.035 to the power of the number of half years in 2 years which is 4.
– Phil H
8 hours ago
I'm confused where you're getting your N value as I thought it was numbers of years divided by interests compounds per year so for the first 2 years wouldn't it be 4000(1.015)^0.5 as it Would be 2 years divided by 4 (quarterly interest compounds)
– John Deer
10 hours ago
I'm confused where you're getting your N value as I thought it was numbers of years divided by interests compounds per year so for the first 2 years wouldn't it be 4000(1.015)^0.5 as it Would be 2 years divided by 4 (quarterly interest compounds)
– John Deer
10 hours ago
No, it's 1.015 to the power of the number of quarters in 2 years which is 8.Then 1.07 to the power of the number of years which is 2 and finally 1.035 to the power of the number of half years in 2 years which is 4.
– Phil H
8 hours ago
No, it's 1.015 to the power of the number of quarters in 2 years which is 8.Then 1.07 to the power of the number of years which is 2 and finally 1.035 to the power of the number of half years in 2 years which is 4.
– Phil H
8 hours ago
add a comment |
John Deer is a new contributor. Be nice, and check out our Code of Conduct.
John Deer is a new contributor. Be nice, and check out our Code of Conduct.
John Deer is a new contributor. Be nice, and check out our Code of Conduct.
John Deer is a new contributor. Be nice, and check out our Code of Conduct.
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1
Far better to use understanding than to use a formula.
– Gerry Myerson
10 hours ago
I get that but I'm struggling with the concept and I think knowing the formula would allow me the context to mentally frame it better.
– John Deer
10 hours ago
I think understanding the mathematics would be a better idea, but each to his/her own.
– Gerry Myerson
10 hours ago
If you would like to try and give me a better understanding I would very much like to hear it.
– John Deer
10 hours ago
1
OK. What's the balance after two years, before the first repayment? What's the balance after two years, after the first reapyment? Same question for after 4 years, before and after the second repayment. Then, what's the balance at the end of six years?
– Gerry Myerson
10 hours ago