Question

Suppose you borrowed $400,000 for a home mortgage on January 1, 2010 with an annual interest rate of 3.5% per year compounded monthly.

(a) If you didn't make any payments and were only charged the interest (and no late fees), how much would you owe on the mortgage on January 1, 2030?

(b) Suppose the balance on the mortgage is amortized over 20 years with equal monthly payments at the end of each month. (This means the unpaid balance on January 1, 2030 should be $0). What are the monthly payments?

(c) How much interest was paid during the 20 years of the mortgage?

(d) What is the unpaid balance on the mortgage on January 1, 2015?

Answer 1

part-(a)

If you didn't make any payments and were only charged the interest

so formula is

P=400000

r=3.5% = 0.035

n=12 for monthly compound

t=20 years

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part-(b)

a mortgage is amortized over 20 years with equal monthly payments

so formula is

P=400000

r=3.5% = 0.035

n=12 for monthly compound

t=20 years

...........monthly payment

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part-(c)

total interest paid is given by

..............total interest paid

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part-(d)

for unpaid balance, formula is

here t= remaining payment

here we want to find the balance of the loan on  January 1, 2015?

so a remaining period is 5 years

so take t=5 years

.........................unpaid balance on the mortgage on January 1, 2015