Chapter 2, Problem 1RE

In Exercises 1–6, find the future value of the investment.

$6,000 for 5 years at 4.75% simple annual interest.

To determine

To calculate: The future value of an investment of $6,000 for 5 years at $4.75\%$ simple annual interest.

Answer to Problem 1RE

Solution:

The future value of an investment of $6,000 for 5 years at $4.75\%$ simple annual interest is $\$7,425.00$.

Explanation of Solution

Given Information:

Amount of $6,000 is invested for 5 years at $4.75\%$ simple annual interest.

Formula used:

The future value of an investment of PV dollars earning simple interest is given by:

$FV=PV\left(1+rt\right)$ or $FV=PV\left(1+in\right)$

Where r is the annual interest rate and t is the time in years,

Also i is the interest rate per period and n is the number of periods.

Calculation:

Consider the provided information, $6,000 is invested for 5 years at $4.75\%$ simple annual interest.

Since, the present value borrowed is $6,000.

Hence, $PV=6,000$

Also, since they are borrowed for a period of 5 years,

$t=5$

And since, the interest rate is $4.75\%$ per year,

Hence, r is given by:

$\begin{array}{c}4.75\%=\frac{4.75}{100}\\ =0.0475\end{array}$

Since, the future value of an investment of PV dollars earning simple interest is given by:

$FV=PV\left(1+rt\right)$ or $FV=PV\left(1+in\right)$

Therefore,

Substitute 6,000 for PV, $5$ for t and $0.0475$ for r in $FV=PV\left(1+rt\right)$.

$\begin{array}{c}FV=\left(6,000\right)\left(1+\left(5\right)\left(0.0475\right)\right)\\ =\left(6,000\right)\left(1+0.2375\right)\\ =\left(6,000\right)\times 1.2375\\ =7,425.00\end{array}$

Thus, the future value of an investment of $6,000 for 5 years at $4.75\%$ simple annual interest is $\$7,425.00$.