Question

Kira has $2,000 to invest today that she wants to grow to $3,000 in five years. What annually compounded rate of interest would she have to receive in order to reach her goal?

A. Roughly 4.6 percent.

B. Roughly 6.5 percent.

C. Roughly 8.4 percent.

D. Roughly 9.3 percent.

Answer 1

To grow $2,000 to $3,000 in 5 years, Kira needs an annually compounded interest rate of roughly 8.4 percent, which is answer C.

Step-by-step explanation:

To determine the necessary annual compound interest rate to grow Kira's investment from $2,000 to $3,000 over five years, we can use the formula for compound interest:

A = P(1 + r)n

Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money).
r = the annual interest rate (decimal).
n = the number of years the money is invested.

Plugging in Kira's values, we get:
$3,000 = $2,000(1 + r)5

To find the interest rate 'r', we need to solve for r in the equation:

1.5 = (1 + r)5

Using a calculator or algebraic methods, we can solve for 'r' and find that it is approximately 0.084, or 8.4%.

Therefore, the answer is C. Roughly 8.4 percent.