A compound interest problem

A

Acecustis

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Here is the problem:

A debt of 25,000 is to be amortized over 7 years at an annual interest rate of 7%. Calculate the value of monthly payments (a) if interest is compounded once a year, and (b) if interest is compounded monthly

I thought the formula for solving this problem was:

A=r*PV/1-(1/1+r)^n

where A=payments period, n=# of periods, PV=present value and r=interest rate.

I'm plugging the numbers in and I'm not getting the right answer. I'm pretty sure I'm using the wrong formula. Please help!
 
The formula isn't that important. Getting the right interest rate is the key. Just find the one that matches the payments.

Monthly Payments / Monthly Compounding

i = 0.07
j = i/12 = 0.0058333333
v = 1/(1+j) = 0.9942004971

25000 = Pmt*(v + v^2 + v^3 + ... + v^84) = Pmt*[(v - v^85)/(1-v)] ==> Pmt = 377.32

Monthly Payments / Annual Compounding

i = 0.07
r = (i+1)^(1/12) = 1.07^(1/12) = 1.0056541454
v = 1/r = 0.9943776442

25000 = Pmt*(v + v^2 + v^3 + ... + v^84) = Pmt*[(v - v^85)/(1-v)] ==> Pmt = 374.69
 
Acecustis said:
Here is the problem:

A debt of 25,000 is to be amortized over 7 years at an annual interest rate of 7%. Calculate the value of monthly payments (a) if interest is compounded once a year, and (b) if interest is compounded monthly

I thought the formula for solving this problem was:

A=r*PV/1-(1/1+r)^n

where A=payments period, n=# of periods, PV=present value and r=interest rate.

I'm plugging the numbers in and I'm not getting the right answer. I'm pretty sure I'm using the wrong formula. Please help!
Click to expand...

Please show us your work. What answer are you getting? How do you know it is wrong?

Mathematically speaking, the formula you used does not make sense - but used in certain way can produce correct result. The correct formula is:

Payment = r∗PV1−(11+r)n\displaystyle Payment \ = \ \frac{r*PV}{1 - \left (\frac{1}{1+r}\right )^n}

The correct way to write that formula would be:

A=r*PV/[1-{1/(1+r)}^n]

or

Payment = r∗PV1−1(1+r)n\displaystyle Payment \ = \ \frac{r*PV}{1 - \frac{1}{(1+r)^n}}

A=r*PV/[1-1/(1+r)^n]
 
tkhunny said:
The formula isn't that important. Getting the right interest rate is the key. Just find the one that matches the payments.

Monthly Payments / Monthly Compounding

i = 0.07
j = i/12 = 0.0058333333
v = 1/(1+j) = 0.9942004971

25000 = Pmt*(v + v^2 + v^3 + ... + v^84) = Pmt*[(v - v^85)/(1-v)] ==> Pmt = 377.32

Monthly Payments / Annual Compounding

i = 0.07
r = (i+1)^(1/12) = 1.07^(1/12) = 1.0056541454
v = 1/r = 0.9943776442

25000 = Pmt*(v + v^2 + v^3 + ... + v^84) = Pmt*[(v - v^85)/(1-v)] ==> Pmt = 374.69
Click to expand...

Thanks for the assistance. But what does "v" represent?
 
Joking, right? It is defined inthe description.
 
Fair enough. Actually, 'v' is rather comon usage for a 1-year discount factor. I tend to use it a bit more generally than that.
 
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