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
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