Question

At the beginning of 2016, Mr. Greenspan decides to take advantage of the low interest rate and takes out a 30-year mortgage loan whose initial principal balance is $300,000. The quoted rate is 2% per annum, and Mr. Greenspan will make payments semi-annually.

(1) What is Mr Greenspan's semi-annual payment?

(2) How much does Mr. Greenspan need to pay toward interest during the second payment period (second half of the first year)?

(3) What is Mr Greenspan's remaining balance at the end of the 5th year (i.e. after both payments during year 5)?

Answer 1

Solution 1)

Principal Balance = $300,000

Loan Term = 30 years i.e. 60 half-years

Interest rate = 2% per annum i.e. 1% per half year

Half yearly payment = 300000*1%/(1-(1+1%)^-60) = $6,673.33

Solution 2)

Interest in First payment = 1% * 300000 = 3000

Principal Payment = $6673.33 – 3000 = $3673.33

Principal outstanding after first payment = $300000 – $3673.33 = $296,326.67

Interest During the second payment = 1% * $296,326.67 = $2,963.27

Solution 3)

Remaining balance at the end of the 5th year = PV of remaining payments

PV of remaining 50 payments = 261568.63 or $261,569

Remaining balance at the end of 5^th year = $261,569