Question

a Financial institution offers a 10 year mortgage at an annual rate of 6% compounded monthly.

a. the monthly payment for $150,000 mortgage?

b. The principle that remain after seven years?

c. the new payment if the interest-rate goes up to 8.4% after seven years

d. The total interest paid on the loan if the interest rate changes as described in part C?

Answer 1

a. Annual rate of 6% Compouded monthly means 6% divided by number of months, we will get one month interest rate

that is .06 / 12 = .005

a. Monthly payment of $ 150000 is the hint to calculate principal amount here we knows monthly interets rate as well as monthly interest amount.

So principal amount should be = Monthly interets amount / Monthly interest rate

= $ 150000 / .005

= $ 30,000,000

c. Principal remain same after seven year means borrower paid only interest.

to calculate seven year interest we need to know number of installment paid by the borrower that is

7 years multiplied by 12 Months we will get number of installment.

= 7* 12

=84 installment

=84* $ 150000

= $12,600,000 (7 year interest paid amount)

d. Interest rate changed to 8.4% from 6% so monthly interest rate will be

= 8.4% / 12

=.007

to get monthly interest payment, firstly we alreay identified principal amount

Principal amount * .007 , we will get monthly interest amount

Principal Amount = $ 30,000,000

= $ 30,000,000 * .007

= $ 210,000 (year 7 to 10 monthly installment)

now we know in last three year there are 36 installment (12* 3)

=$ 210,000* 36

=$ 7,560,000

Total interest payment will be =$12,600,000 + $ 7,560,000

=$ 20,160,000

Kindly let us know if further queries.

Thanks.