Eugene began to save for his retirement at age 32, and for 10 years he put $ 275

Question

Eugene began to save for his retirement at age 32, and for 10 years he put $ 275 per month into an ordinary annuity at an annual interest rate of 8% compounded monthly. After the 10 years, Eugene was unable to make the monthly contribution of $ 275, so he moved the money from the annuity into another account that earned 8% interest compounded monthly. He left the money in this account for 23 years until he was ready to retire. How much money did he have for retirement?

Retirement amount =

If Eugene had waited until he was 45 years old to start saving for retirement and then decided to put money into an ordinary annuity for 20 years earning 8% interest compounded monthly, what monthly payment would he have to make to accumulate the same amount for retirement as you found in the first part of the question?

Retirement amount =

Explanation / Answer

Eugene began to save for his retirement at age 32, and for 10 years he put $ 275 per month into an ordinary annuity at an annual interest rate of 8% compounded monthly. After the 10 years, Eugene was unable to make the monthly contribution of $ 275, so he moved the money from the annuity into another account that earned 8% interest compounded monthly. He left the money in this account for 23 years until he was ready to retire. How much money did he have for retirement?

Retirement amount = Monthly Contribution*((1+r/12)^(12*10) - 1)/(r/12) * (1+r/12)^(12*23)

Retirement amount = 275*((1+8%/12)^(12*10) - 1)/(8%/12) * (1+8%/12)^(12*23)

Retirement amount = $ 314,851.41

If Eugene had waited until he was 45 years old to start saving for retirement and then decided to put money into an ordinary annuity for 20 years earning 8% interest compounded monthly, what monthly payment would he have to make to accumulate the same amount for retirement as you found in the first part of the question?

Retirement amount =$ 314,851.41

Monthly payment = Retirement amount /(((1+r/12)^(12*20) - 1)/(r/12))

Monthly payment = 314,851.41/(((1+8%/12)^(12*20) - 1)/(8%/12))

Monthly payment = $ 534.53

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