STRATEGY 1: SAVINGS EARLY PLAN

Question

Assume that you are 22 years old and started saving for retirement on January 1, 2022. You plan to retire on December 31, 2064, when you are 64 years old. There are 43 years from the time you started investing (saving) until you retire. You have no previous or other retirement savings when you start to save. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

 

You invest $250 at the end of each month into a retirement account paying 8.75% compounded monthly from January 1, 2022, until you retire. Show all work and answer the following questions:

 

1. Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 43 years?
2. Assuming you made all the monthly payments for 43 years, how much did you pay into your retirement account?
3. Assuming you made all the monthly payments for 43 years, how much interest did you earn over the 43 years?

Answer 1

The question requires the calculation of the Future Value of Money. The monthly contributions are an annuity.

Future Value of Annuity = P * ([1 + I]^N - 1 )/I,

where P is the payment amount.

I is equal to the interest (discount) rate.

N is the number of payments

=250 * ((1+8.75%/12)^(43*12)-1)/(8.75%/12)

FV = 1,421,902.73

B.Amount paid to retirement account = Payment amount * number of payments

=250*12*43 = 129,000

C. Interest earned = FV minus amount paid to the retirement account

= 1,421,902-129000

= 1,292,902.73