Question

If the initial investment is $10,000 and the amount to be received in the future from this investment at the end 14 years $19,799, what is implied rate of return on that investment? Completely and precisely show how you applied the correct table to solve this problem.

Answer 1

The implied rate of return is found using the formula for compound interest. By substituting the known future value, present value, and the number of years, we solve for the annual rate. The calculated annual rate of return for the $10,000 investment over 14 years is 5%.

Step-by-step explanation:

The problem presented requires us to find the implied rate of return on an investment using the formula for compound interest. We have an initial investment of $10,000, and the future value after 14 years is $19,799. The general formula for compound interest is given by:

FV = PV (1 + r)^n

Where:

• FV = future value of the investment
• PV = present value of the investment (initial investment)
• r = annual interest rate
• n = number of years

Plugging in the known values we get:

19,799 = 10,000 (1 + r)^14

To solve for the rate r, we need to isolate it:

(1 + r)^14 = 19,799 / 10,000

(1 + r)^14 = 1.9799

We can then apply the 14th root to both sides to solve for (1 + r):

1 + r = (1.9799)^(1/14)

Now, using a calculator:

1 + r = (1.9799)^(1/14) ≈ 1.0500

r = 1.0500 - 1

r = 0.0500 or 5%

The implied annual rate of return on the investment over 14 years is 5%.