Question

To make CDs (certificates of deposit) look more attractive than they really are, some banks advertise that their rates are higher than their competitors’ rates; however, the fine print says that the rate is a nominal interest rate. If a person deposits $10,000 at 10% per year nominal interest, what effective interest rate, compounded continuously, would yield the same amount of money in 3 years?

Answer 1

r = 9.14%

Step-by-step explanation:

Simple interest = P * (1+rt)

Simple interest = $10,000 * (1+0.10 * 3)

Simple interest = $10,000 * 1.3

Simple interest = $13,000

Calculating the compound interest rate

A = P*(1+r)^n

$13,000 = $10,000 * (1+r)^3

(1+r)^3 = $13,000 / $10,000

r =
`\sqrt[3]{$13,000/ $10,000 - 1}`

r = 0.0914

r = 9.14%