Question

Benjamin invested $66,000 in an account paying an interest rate of 63%

compounded annually. Christian invested $66,000 in an account paying an interest
rate of 5% compounded continuously. After 19 years, how much more money would
Benjamin have in his account than Christian, to the nearest dollar?

Answer 1

$16,755

Explanation:

You want the difference in interest earned on $66,000 after 19 years between an account earning 6 3/8% compounded annually, and one earning 5 3/4% compounded continuously.

Interest formulas

The formula for the account value multiplier when interest is compounded annually is ...

k = (1 +r)^t . . . . . . compounded annually at rate r for t years

When interest is compounded continuously, the multiplier is ...

k = e^(rt)

Application

The difference in account values between the two rates is ...

∆value = $66,000·(1 +0.06375)^19 -e^(0.0575·19))

∆value ≈ $16,754.70

Benjamin will have about $16,755 more than Christian after 19 years.