Question

A fully amortized mortgage is made for $100,000 for 10 years. Interest rate is 6 percent per year compounded monthly.

1. What is the monthly payment amount?
2. What is balance of the loan at the end of 5 years?
3. What is the total interest paid by the end of the fifth year?
4. What is the total principal paid by the end of the tenth year?

SHOW WORK AND DONT USE EXCEL

Answer 1

t = 10 * 12 = 120 months

i = 6% / 12 = 0.5% per month

a.

Monthly loan payment = 100000*(A/P,0.5%,120)

= 100000 *0.005*((1 + 0.005)^120)/((1 + 0.005)^120-1)

= 100000 *0.005*((1.005)^120)/((1.005)^120-1)

= 100000 * 0.011102

= 1110.20

b.

No of installments remaining after 5 yrs = 120 - 60 = 60

Balance principal = 1110.20 * (P/A,0.5%,60)

= 1110.20 * ((1 + 0.005)^60-1)/(0.005 * (1 + 0.005)^60)

= 1110.20 * ((1.005)^60-1)/(0.005 * (1.005)^60)

= 1110.20 * 51.725561

= 57425.72

c.

Principal paid until end of fifth yr = 100000 - 57425.72 = 42574.28

interest paid = 1110.20 * 60 - 42574.28 = 24037.72

d.

As loan term is 10 yrs, principal paid by end of 10 yr = 100000 (loan will be paid off)