400,000 for retirement in 30 years the account earns 8% interest. how would I need to deposit each month how much interest will I earn

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
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400,000 for retirement in 30 years the account earns 8% interest.

how would I need to deposit each month

how much interest will I earn? 

Expert Solution
Answer 1

Future Value (Required for retirement) = 400,000

Since monthly deposits

Time Period = 30 years * 12 = 360 months

Interest = 8%/12 = 0.6667%

 

Future Value = [(Monthly Deposit)*(1+interest%)^359]+[(Monthly Deposit)*(1+interest%)^358]+[(Monthly Deposit)*(1+interest%)^357]+[(Monthly Deposit)*(1+interest%)^356]+[(Monthly Deposit)*(1+interest%)^355]+[(Monthly Deposit)*(1+interest%)^354]+[(Monthly Deposit)*(1+interest%)^353]+...................................................+[(Monthly Deposit)*(1+interest%)^0]

400,000= ((Monthly Deposit)*(1.006667)^359)+((Monthly Deposit)*(1.006667)^358)+((Monthly Deposit)*(1.006667)^357)+((Monthly Deposit)*(1.006667)^356)+((Monthly Deposit)*(1.006667)^355)+((Monthly Deposit)*(1.006667)^354)+.....................................+((Monthly Deposit)*(1.006667)^0)

Monthly Deposit = 268.39

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