### Home > APCALC > Chapter 5 > Lesson 5.3.1 > Problem5-116

5-116.

When interest is compounded quarterly, the annual percentage rate is split into four equal parts and distributed four times during the year, at equally spaced time intervals. Compounding yields more money, because interest is earned on previous interest. The easiest way to compute the amount of money in an account after an interest period is by multiplying the old amount by a number, which we will call the multiplier. What multiplier applies to each of the following situations? (Give both the unsimplified and the simplified forms.)

Example: $6\%$ annual interest compounded quarterly

Solution: Unsimplified: $1+\frac{0.06}{4}$ Simplified: $1.015$

1. $6\%$ annual interest compounded twice a year

$1+\frac{0.06}{2}\approx 1.03$

2. $6\%$ annual interest compounded monthly

$1+\frac{0.06}{?}\approx \underline{ \ \ \ \ \ \ \ \ }$

3. $6\%$ annual interest compounded daily

Refer to model problems and the example above.