Question

Jack borrows $500,000 for 10 years at a fixed interest rate of i % p.a (EAR). If the debt is repaid in equal year-end payments over the 10 years, the amount of interest Jack pays in the first 5 years (years 1 to 5): Select one:

a. Is less than the interest paid in the last 5 years

b. Is greater than the interest paid in the last 5 years

c. Is equal to the interest paid in the last 5 years

Answer 1

Loan period = 10 years,

As it is given that loan or debt is being repaid in equal year end payments over 10 years and rate of interest is fixed over term of the loan. Therefore it can be said the loan is a fully amortizing loan with equal annual payments. In the fully amortization loan, equal annual payments consist of both interest and principal payments.

We know that interest for a year = Outstanding balance of loan at beginning of a year x interest rate

As loan is being repaid, outstanding balance of loan at beginning of a year is reduced each year due to yearly principal payments. Due to this interest paid on the loan will also reduced year on year. Interest paid for a year is always less than the interest paid for previous year.

Thus sum of interest paid for first five years will be greater than sum of interest paid for last 5 years

Answer: b. Is greater than the interest paid in the last 5 years