Chapter 6, Problem 6.1CTF

Two years ago, you opened an investment account and deposited $5,000. One year ago, you added another $2,000 to the account. Today, you are making a final deposit of $7,500. How much will you have in this account three years from today if you earn a 14 percent rate of return?

Summary Introduction

To calculate: The present value at 14% for 3 years

Introduction:

The present value of future cash flows that is discounted at a particular rate of discount is called as present value.

Answer to Problem 6.1CTF

Person X will have $24,116.57 in his account after three years from the present.

Explanation of Solution

Given information:

Person X has opened an investment account in which he had deposited $5,000 before two years and added $2,000 to it before one year. Presently, he made a final deposit of $7,500. The return rate is 14%.

Formula to calculate the future value:

$\text{Future cash flow}=\text{PV}{\left(1+\text{r}\right)}^{\text{t}}$

Note: PV denotes the present value, r denotes the rate of discount and t denotes the number of years.

Compute the future value:

$\begin{array}{c}\text{Future cash flow}=\text{PV}{\left(1+\text{r}\right)}^{\text{t}}\\ =\$5,000{\left(1+0.14\right)}^5+\$2,000{\left(1+0.14\right)}^4+\$7,500{\left(1+0.14\right)}^3\\ =\$5,000\left(1.925414582\right)+\$2,000\left(1.68896016\right)+\$7,500\left(1.481544\right)\end{array}$

$\begin{array}{c}=\$9,627.072912+3,377.92032+11,111.58\\ =\$24,116.57\end{array}$

Hence, the future cash flow is $24,116.57.