Question

An initial deposit of $45,000 grows at an annual rate of 10% for 20 years. Compare the final balances resulting from continuous compounding and annual compounding. (Round your answers to the nearest cent.)

Answer 1

Annual: $302 737.50

Continuous: $332 507.52

Explanation:

A. Compounded annually

The formula for compound interest is

A = P(1 + r)ⁿ

Data:

P = $45 000

r = 10 %

t = 20 yr

Calculations:

n = 20

A = 45 000(1+ 0.10)²⁰

= 45 000 × 1.10²⁰

= 45 000 × 6.727 499 95

= $302 737.50

B. Compounded continuously

The formula for continuously compounded inerest is

`A = Pe^(rt)`

`A = 45 000e^(0.10 *20)`

`= 45 000e^(2.0)`

= 45 000 × 7.389 056 61

= $332 507.52