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Finite Mathematics

7th Edition
Stefan Waner + 1 other
ISBN: 9781337280426
Textbook Problem

Retirement Planning OHaganBooks.com has just introduced a retirement package for its employees. Under the annuity plan operated by Sleepy Hollow, the monthly contribution by the company on behalf of each employee is $800. Each employee can then supplement that amount through payroll deductions. The current rate of return of Sleepy Hollow’s retirement fund is 7.3%. Use this information in Exercises 45–52.

(See Exercise 45.) Jane Callahan actually wants to retire with $500,000. How much should she contribute each month to the annuity?

To determine

To calculate: The amount that Jane Callahan’s should contribute each month to retire with $500,000 in the retirement fund.

Explanation

Given Information:

OHaganBooks.com introduce a retirement package for its employees. Under the annuity plan, the monthly contribution by the company on behalf of each employee is $800. Each employee can then supplement the amount through payroll deductions. The current rate of return of Sleepy Hollow’s retirement fund is 7.3%.

Jane Callahan plans to retire in 10 years and she contributes $1,000 per month to the plan. Currently, there is $50,000 in her retirement annuity but she wants to retire with $500,000 in her retirement fund.

Formula used:

The future value of an investment of PV dollars earning compound interest at a rate of i per compounding period for n periods is given by:

FV=PV(1+i)n or FV=PV(1+rm)mt

The monthly payments required of the account after n periods is given by:

PMT=FVi(1+i)n1

Calculation:

Consider the provided information:

OHaganBooks.com introduce a retirement package for its employees. Under the annuity plan, the monthly contribution by the company on behalf of each employee is $800. Each employee can then supplement the amount through payroll deductions. The current rate of return of Sleepy Hollow’s retirement fund is 7.3%.

Jane Callahan plans to retire in 10 years and she contributes $1,000 per month to the plan. Currently, there is $50,000 in her retirement annuity but she wants to retire with $500,000 in her retirement fund.

Since, currently, there is $50,000 in the retirement annuity.

PV=50,000

Also, Jane Callahan plans to retire in 10 years,

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

n=10×12=120

The current rate of return of Sleepy Hollow’s retirement fund is 7.3%.

Hence, i is given by:

7.3=7.3100=0.073

Since there are 12 periods,

i=0.07312

The future value of an investment of PV dollars earning compound interest at a rate of i per compounding period for n periods is given by:

FV=PV(1+i)n or FV=PV(1+rm)mt

Substitute 50,000 for PV, 120 for n and 0

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