When you retire at 65, you wish to be able to have $3,000 each month for 25 years. How much would you have to deposit into an account each month, starting when you are 23, if the account earns 7.6% compounded monthly?
When you retire at 65, you wish to be able to have $3,000 each month for 25 years. How much would you have to deposit into an account each month, starting when you are 23, if the account earns 7.6% compounded monthly?
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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When you retire at 65, you wish to be able to have $3,000 each month for 25 years. How much would you have to deposit into an account each month, starting when you are 23, if the account earns 7.6% compounded monthly?
Expert Solution

Step 1
Firstly calculate the present value of annuity with $3000 as PMT and 25 years, use this present value as future value and compute for PMT
Present Value of annuity = PMT * [(1 - 1 / (1 + r)^n)] / r
Where,
PMT = monthly payment
r = rate of interest per period i.e. 7.6%/12 = 0.633%
n = no. of compounding period 25* 12 = 300
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