Question:
Fran Smith has two investment opportunities. The interest rate for both investments is 8%. Interest on the
first investment will compound annually while interest on the second will compound quarterly. Which
investment opportunity should Fran choose? Why?
Answer:
Fran should choose the second investment opportunity. More rapid compounding has the effect of
increasing the actual rate, which is called the effective rate, at which money grows per year. For the
second opportunity, there are four, three-month periods paying interest at 2% (one-quarter of the annual
rate). $10,000 invested will grow to $10,824 ($10,000 x 1.0824*). The effective annual interest rate,
often referred to as the annual yield, is 8.24% ($824 ÷ $10,000), compared to just 8% for the first
opportunity.
Future value of $1: n = 4, i = 2% (from Table 1)
Fran Smith has two investment opportunities. The interest rate for both investments is 8%. Interest on the
first investment will compound annually while interest on the second will compound quarterly. Which
investment opportunity should Fran choose? Why?
Answer:
Fran should choose the second investment opportunity. More rapid compounding has the effect of
increasing the actual rate, which is called the effective rate, at which money grows per year. For the
second opportunity, there are four, three-month periods paying interest at 2% (one-quarter of the annual
rate). $10,000 invested will grow to $10,824 ($10,000 x 1.0824*). The effective annual interest rate,
often referred to as the annual yield, is 8.24% ($824 ÷ $10,000), compared to just 8% for the first
opportunity.
Future value of $1: n = 4, i = 2% (from Table 1)
