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7th Edition

Stefan Waner + 1 other

Publisher: Cengage Learning

ISBN: 9781337280426

Chapter 2.3, Problem 46E

Textbook Problem

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**Retirement Plans and Trusts** Exercises 45–54 are based on the following table, which shows the average returns for some of the largest mutual funds commonly found in retirement plans.^{20} *(Assume end-of-month deposits and withdrawals and monthly compounding, and assume that the quoted rate of return continues indefinitely.)*

Mutual Fund |
Fidelity Growth company |
Vanguard 500 Index |
PIMCO Total Return |
Vanguard Total Bond Market Index |

Rate of Return |
14.83% | 13.25% | 2.77% | 2.67% |

Type |
Stock fund | Stock fund | Bond fund | Bond fund |

How much would be accumulated after 25 years in a retirement account invested entirely in the Vanguard stock fund with payments of $380 per month? [**hinT:** See Quick Example 1.]

To determine

**To calculate:** The amount accumulated after 25 years in a retirement account invested entirely in the Vanguard stock fund with payments of $380 per month.

**Given Information:**

In a retirement account, money is invested entirely in the Vanguard stock fund with payments of $380 per month.

The following table shows the average return for some of the largest mutual funds commonly found in the retirement account:

**Formula used:**

Suppose the payment *PMT* at the end of each compounding period into an account with an interest rate of *i* per period. Then the future value of the account after *n* periods is given by:

**Calculation:**

Consider the provided information, “In a retirement account, money is invested entirely in the Vanguard stock fund with payments of $380 per month.”

Since, the amount invested is $380,

Hence,

Also, since they are invested for a period of 25 years,

In order to convert it into months, multiply by 12.

According to the table,

Since they are invested in Vanguard stock fund,

And since, the rate of return is

Hence, *i* is given by:

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