Question

Consider a 20-year, $175,000 mortgage with an interest rate of 5.65 percent. After six years, the borrower (the mortgage issuer) pays it off. How much will the lender receive? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

This is a sum on equated loan installments.

We find the equal installments by using the present value of annuity formula

Loan Installment = Loan Amount / PVAF(r,t)

PVAF or present value annuity factor is the sum of discounting factors at a given rate 'r' at 't' number of years.

It is given as = (1 - (1/(1+r)^t)) / r

Now,

Loan Installment = 175000 / PVAF(5.65%,20 years) = 175000 / 11.8031 = $14,826.66

Now let us make a schedule of Loan amortization to find out the outstanding balance at the end of 6 years:

Years	Opening Value	EMIs	Interest (Opening Value x 5.65%)	Principal Value (EMI - Interest)	Closing Value
1	1,75,000.00	14,826.66	9,887.50	4,939.16	1,70,060.84
2	1,70,060.84	14,826.66	9,608.44	5,218.22	1,64,842.62
3	1,64,842.62	14,826.66	9,313.61	5,513.05	1,59,329.57
4	1,59,329.57	14,826.66	9,002.12	5,824.54	1,53,505.03
5	1,53,505.03	14,826.66	8,673.03	6,153.63	1,47,351.40
6	1,47,351.40	14,826.66	8,325.35	6,501.31	1,40,850.09

Thus,

Outstanding Amount that the lender will receive = $140,850.09