unpaid balance

Question

Find the unpaid balance on the debt. (Round your answer to the nearest cent.)
After 7 years of monthly payments on $160,000 at 3% for 25 years.

Answer 1

Hi Arron,

 

This problem is most easily worked if thought of as two annuities.

 

First, we need to find the monthly payment that will payback the $160,000 at 3% interest with monthly payments for 25 years, similar to a $160,000 mortgage at 3%.

 

Terms:

 

Monthly interest rate (i) =  annual rate =.03/12 = .0025

Number of compounding periods (n) = Term * 12  = 300 compounding periods

PMT = monthly payment

PV = present value

 

First, we need to find the monthly payment using the ordinary annuity formula for the present value.

 

PV = PMT * (1/i)*(1-1/(1+r)^n) or PMT*(1/.0025)*(1-1/(1.0025)^300)

 

Solve for PMT gives us

 

PMT = $160,000/(1/.0025)*(1-1/(1.0025)^300) = $758.74 per month

 

In order to find the balance after 7 years, we simply need to find the present value of 25 -7 or 18 years of cash flows.

 

now n = 18*12 or 216 payments so that the balance is just the present value of 216 payments discounted at .25%

 

PV= PMT *(1/.0025)*(1-1/(1.0025)^216) = $758.74 *  166.7435658 = $126,515.01

 

Hope this helps,

 

 

 

Answer 2

FV = PV(1 + r)ⁿ - P[((1 + r)ⁿ - 1) / r]

FV = future value

PV = original value

r = rate

n = number of calculations

P = monthly payments

 

Substitute data and calculate.