# You are depositing $1,500 in a retirement account today and expect to earn an average return of...

## Question:

You are depositing $1,500 in a retirement account today and expect to earn an average return of 7.5 percent on this money. How much additional income will you earn if you leave the money invested for 45 years instead of just 40 years?

## Future Value:

This question requires an understanding of the time value of money (TVM), a concept which holds that a dollar today is worth more than a dollar in the future, because of its ability to earn interest and grow over time. In finance, the TVM takes the form of a discount rate. Moreover, the future value (FV) of an investment is the present value (PV) of the investment compounded into the future, using the interest rate.

## Answer and Explanation: 1

You will earn $11,790.90 more ($38,857.26 - $27,066.36), if you leave the money invested for 45 years.

This problem entails computing and comparing the FVs of the $1,500 investment, using the 7.5% rate and time periods provided.

Mathematically, this is accomplished with the following formula:

FV = PV * (1+r)^(t)

Where,

t = years

r = discount rate

PV = present value

Using the variables provided, the future value of the each scenario is computed as follows:

(1) FV = 1,500 * (1+.075)^40 = $27,066.36

(2) FV = 1,500 * (1+.075)^45 = $38,857.26

$38,857.26 - $27,066.36 = $11,790.90

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Chapter 5 / Lesson 16Understand the definition of future value and the future value formula. Explore some examples that show how to calculate the future value of an investment.

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