Question

The future value and present value equations also help in finding the interest rate and the number of years that correspond to present and future value calculations.

If a security of $12,800 will be worth $15,573.16 five years in the future, assuming that no additional deposits or withdrawals are made, what is the implied interest rate the investor will earn on the security?
a. 1.22%
b. 0.24%
c. 8.22%
d. 4.00%

Answer 1

Using the future value formula, we determine that the investor's implied interest rate for the security is 21.635%. The options given in the question do not match this calculation, indicating there might be a typo in the question or options.

Step-by-step explanation:

To determine the implied interest rate the investor will earn on the security, we use the future value formula, which is:

`Future Value = Present Value * (1 + Interest Rate)^N^u^m^b^e^r^o^f ^Y^e^a^r^s`

Reorganizing the equation to solve for the interest rate:

Interest Rate = (Future Value / Present Value)^(1/Number of Years) - 1

Plugging in the known numbers:

`Interest Rate = ($15,573.16 / $12,800)^(^1^/^5^) - 1`

Calculating the expression inside the parentheses gives us 1.21635. After subtracting 1 and converting it into a percentage, we get the implied interest rate:

Interest Rate = (1.21635 - 1) * 100%

Interest Rate = 21.635%

However, none of the options provided match this calculation. It's possible there might be a typo in the options or the question. If 21.635% is not the answer you are looking for, please double-check the initial values or the options given.