You deposit $3,000 into an N-year certificate of deposit that pays 4.5 percent annual interest, and at the end of the N years you have $3,738.54. What is the number of years, N?
A)4
B)5
C)6
D)7

Question

Quizplus · Accepted Answer

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final amount ($3,738.54)
P = the principal amount ($3,000)
r = the annual interest rate (4.5%/100 = 0.045)
n = the number of times interest is compounded per year (assuming annual compounding, n = 1)
t = the number of years

Plugging in the values we know, we get:

$3,738.54 = $3,000(1 + 0.045/1)^(1N)

Simplifying:

1.24618 = (1.015)^N

Taking the logarithm of both sides:

N = log(1.24618) / log(1.015) = 4.96

Since N represents the number of whole years, we round up to N = 5.

Therefore, it will take 5 years for the deposit to grow to $3,738.54.

You Deposit $3,000 into an N-Year Certificate of Deposit That