Question

You are considering between two loans. Assume everything between these two loans is the same except for the interest rate. Loan A offers 5.5% compounded weekly. Loan B offers 5.64% compounded semiannually. Which loan is better and why?

		Loan A because the actual rate is 5.65% is lower than Loan B’s actual rate.
		Loan A because 5.5% is lower than Loan B’s 5.64%.
		Loan B because the actual rate is 5.72% is higher than Loan A’s actual rate.
		Loan B because 5.64% is higher than Loan A’s 5.5%.
		None of the above.

Answer 1

Given:
Loan A with interest rate 5.5% compounded weekly
Loan B with interest rate 5.64% compounded semi annually.

To compare which one is better, we first need to find the actual rate of these loans. Actual rate is also called Effective rate. And we have a formula for Effective rate.

Where,
E = Effective interest rate
i = interest rate
n = number of years
a = number of compounding in a year.

For Loan A:

In a year there are 52 weeks

OR

For Loan B:

Semiannually means compounded twice a year.

OR

So, Actual rate of loan A is 5.65% and that of loan B is 5.72%. Interest rate is borrowing cost of loan, so lower cost is better.

Therefore, Option 1 is correct. "Loan A because the actual rate is 5.65% is lower than Loan B’s actual rate."