$15,000 is invested into an account that earns interest at j₄ = x%.There are no other deposits made into the account.At the end of 15 years,the accumulated value of the account is $45,000.Determine x.

Question

Quizplus · Accepted Answer

We can use the formula for compound interest to solve for x:

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

Where:
A = accumulated value = $45,000
P = principal = $15,000
r = annual interest rate in decimal form (what we're trying to find)
n = number of times compounded per year (we're not given this information, so we will assume it is compounded annually)
t = time in years = 15

Plugging in these values, we get:

$45,000 = $15,000(1 + r/1)^(1*15)

Simplifying:

3 = (1 + r)^15

Taking the 15th root of both sides:

1 + r = 1.0739

r = 0.0739

Converting to a percentage:

r = 7.39%

Therefore, the answer is (C).

$15,000 Is Invested into an Account That Earns Interest at J4

$15,000 Is Invested into an Account That Earns Interest at J₄