Question

Q2. (a) Abu just borrowed RM30,000 to pay for a second hand car from UTAR Bank. He took out a 60-month loan at an interest rate of 10.472% per annum and his installment payments are RM761.80 per month. The UTAR Bank’s loan officer showed the following calculations to Abu on how the monthly installment payments are derived: Total interest to be paid = 10.472% x RM30,000 x 5 years = RM15,708 Total interest and principal to be paid = RM15,708 + RM30,000 = RM45,708 Monthly instalment = RM45,708 / 60 months = RM761.80
Abu feels that he is effectively paying much more than 10.472% per annum
for the abovementioned loan but he does not know how to calculative effective
annual interest rate. Evaluate whether Abu’s suspicion is indeed justified or
not.

(b) Your parents have decided to sell their home, and they ask you what their
current mortgage balance is. In addition, they also want to know how much
interest and principal have they paid for the last 15 years. They took out a
$125,000 mortgage 15 years ago with an original term of 25 years at 8%
interest rate.

(c) Differentiate between effective annual rate (EAR) and annual percentage rate
(APR). Explain the effect on EAR when interest is compounded more
frequently.

Answer 1

Q2(a):

The monthly payment of RM761.80 does not take care of periodical repayments of principal and hence does not reflect the true interest rate paid. Effective Annual Interest rate of the given case is 19.561693% as follows:

Q2(b):

Present mortgage balance= $79,517.79

Total interest and principal paid in 15 years= $128,176.44

Principal repaid in 15 years= $45,482.21

Total of interest and principal paid in 15 years= $173,658.65

Calculation as below:

Q2(c):

Effective Annual Rate(EAR) is the simple rate of interest representing the actual amount of return during the period. To make it simple, it is the total amount of interest on a deposit or loan, applicable for the period of one year, as a percentage of principal. The amount of interest taken for this purpose could contain compounding effect within the period, but the same is converted into the form of rate in the Effective Annual Rate.

Annual Percentage Rate (APR) is the cost of borrowing per year or income earned from an investment per year, expressed as percentage of Principal. APR may contain fees and other charges along with interest and is the rate quoted, to be applied with or without compounding at the desired/ stated frequency. On the other hand, EAR is the statement of cost as a rate, including the effect of compounding, if any.

Since compounding involves adding interest on interest, EAR will be gigher when frequency of compounding within a year is higher.