# How much will your corporation have accumulated in the trust funds account for its retired...

## Question:

How much will your corporation have accumulated in the trust funds account for its retired employees at the end of 20 years from now, if it deposits $20,000 at the beginning of the first year, and $5,000 at the end of each year thereafter, with the last deposit made at the end of the 20th year? Assume the firm can earn a sure 6% annual interest rate (return) on the deposited money.

Calculate the Future Value of all of the cash flows at the end of year 20.

## Future value:

It refers to the total value that will be accumulated in the account on the maturity of an investment. If the rate of interest is high, the accumulated amount shall be high. Generally, investments of longer maturities pay a higher rate of returns.

## Answer and Explanation: 1

Future value of annuity will be calculated in two parts one for annuity of 19 years and another for initial investment of $20,000 as shown below:

{eq}\begin{align*} {\rm\text{Future value of annuity}} &= {\rm\text{P}}{\left( {1 + {\rm\text{r}}} \right)^{\rm\text{n}}} + {\rm\text{Annuity}} \times \left( {\frac{{{{\left( {1 + {\rm\text{r}}} \right)}^{\rm\text{n}}} - 1}}{{\rm\text{r}}}} \right)\\ &= \$ 20,000{\left( {1 + 0.06} \right)^{20}} + \$ 5,000 \times \left( {\frac{{{{\left( {1 + 0.06} \right)}^{19}} - 1}}{{0.06}}} \right)\\ &= \$ 232,942.67 \end{align*} {/eq}

This amount will further be increased by $5,000 as the last deposit was made at the end of year 20.

Thus, no interest will be earned on the last deposit and the accumulated amount shall be $237,942.67

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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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