Question

To finance the purchase of a new home, a homebuyer takes-out a fully amortizing loan in the amount of $500,000 at 9% interest per year, compounded monthly, for a term of 20 years.

1. What is the outstanding balance of the loan at the end of 5 years?

2. At the end of year 5, the market rate of interest is 6%. What is the market value of the loan at the end of 5 years?

3. If this loan is sold at market value at the end of year 5, is this loan sold at a discount?

use financial calculator, explain why please.

Answer 1

1. Principal value of loan (P) = $ 500000

Rate of interest (r) = 9% p.a. i.e, 0.75% per month (9/12).

No. of months (m) = 12*5 = 60

To compute Outstanding balance of loan at end of 5 years,

A = P(1+r)^n

=500000(1+0.0075)^60

= $ 782840.5

2. Since, at the end of year 5, the market value of interest has fallen to 6%, Loan value at mkt interest rate :

P=500000

n= 15 years*12 months= 130 months remaining for the loan to become repayable

r = 6/12 = 0.5% per month

A = P(1+r)^n

=500000(1+0.005)^130

= $ 956220

3. Loan value after 5 years at current interest rate :

P=500000

r=0.75% per month

n= 15 years*12 months.

A = P(1+r)^n

=500000(1+0.0075)^130

= $ 1320770

Hence, if the loan is sold at the end of 5 years at Market value of $ 956220 on the date of sale, compared to value of $ 1320770, it will be cosidered as sold for discount since the realising value (market value) would be lower than the value of loan in respect of current interest rate on loan at which it is purchased. Market value would be lower due to fall in interest rate in future, making the valuation of loan lower for the remaining 15 years, from the expiry of 5 years, compared to current committed rate of interest.