Question

If an investment worth $2000 is expected to be worth $2809.86 three years in the future, what is the implied interest rate the investor will earn on the investment? A) 13.6% B) 18.5% C) 9.25% D) 11.2%

Answer 1

The implied interest rate the investor will earn on the investment is 12.3%.

Option (D) is true.

Explanation:

To find the implied interest rate on the investment, we can use the formula for compound interest:

Future value = Present value * (1 + interest rate)^n

Given that the present value (PV) is $2000, the future value (FV) is $2809.86, and the time period (n) is 3 years, we can rearrange the formula to solve for the interest rate (r):

Interest rate = ((FV / PV)^(1/n)) - 1

Let's substitute the given values into the formula and calculate the interest rate:

Interest rate = (($2809.86 / $2000)^(1/3)) - 1

= (1.40493^(1/3)) - 1

Using a calculator, we can evaluate this expression:

Interest rate ≈ 1.123 - 1

≈ 0.123

To convert this into a percentage, we multiply by 100:

Interest rate ≈ 0.123 * 100

≈ 12.3%

Therefore,

Option (D) is true.