Question

In: Finance

1. Suppose you wish to buy a house for $500,000. You make a 25% down payment...

1. Suppose you wish to buy a house for $500,000. You make a 25% down payment and borrow the rest at an interest rate of 6% for 30 years.

(a) What is your annual repayment?

(b) Repeat the above assuming a mortgage term of 25 years.

2. Suppose you borrow $20,000 to buy a car. The interest rate is 11% and the loan is for 8 years.

(a) What is your annual repayment?

(b) What is the remaining balance after 3 years?

(c) What is the remaining balance after 7 years?

Solutions

Expert Solution

Answer 1 (a):

Borrowings = Price of house - down payment = 500000 - 25% * 500000 = $375,000

Interest rate = 6%

Time periods = 30 years

To get annual payment, we will use PMT function of excel:

= PMT (rate, nper, pv, fv, type)

= PMT (6%, 30,-375000, 0, 0)

= 27243.3418

= $27,243.34

Annual repayment = $27,243.34

Answer 1 (b):

Time periods = 25 years

= PMT (6%, 25,-375000, 0, 0)

= 29335.0193296

= $29,335.02

Annual repayment = $29,335.02

Answer 2(a):

Borrowing = $20,000

Interest rate = 11%

Time period = 8

= PMT (11%, 8,-20000, 0, 0)

= 3886.421084

= $3,886.42

Annual repayment = $3,886.42

Answer 2(b)

Remaining balance after 3 years = PV of remaining annual installments

= PV (rate, nper, pmt, fv, type)

= PV (11%, 5, -3886.421084, 0, 0)

= $14,363.81

Remaining balance after 3 years = $14,363.81

Answer 2(c):

Remaining balance after 7 years = PV of remaining annual installments

= 3886.421084 / (1 + 11%)

= $3,501.28

Remaining balance after 7 years = $3,501.28​​​​​​​

jeff jeffy answered 2 years ago
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