Question

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

- What is the monthly payment amount?
- What is balance of the loan at the end of 5 years?
- What is the total interest paid by the end of the fifth year?
- 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)

SHOW CLEAR WORK ON EXCEL
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