Question

You are 30 years old and decide to start saving for your retirement. You plan to save $ 5000 at the end of each year (so the first deposit will be one year from now), and will make the last deposit when you retire at age 65 Suppose you earn 11 % per year on your retirement savings. a. How much will you have saved for retirement?

b. How much will you have saved if you wait until age 39 to start saving (again, with your first deposit at the end of the year)?

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Answer #1

a) Age = 30 years.

Annuity = $ 5000 at the end of each year

Retirement age = 65 years

Interest = 11 % pa.

Number of Annuity payments made = 65 - 30 = 35 years

**Calculation of saving for retirement**

FV = A((1+r)^n -1) / r

where A = annuity

r = Interest rate

n = Time period

FV = 5000((1+0.11)^35 -1) / 0.11

FV = 5000(38.5748510 -1) / 0.11

FV = 5000(37.5748510) / 0.11

FV = 5000 * 341.5895548

**FV = $ 1,707,947.77**

**Saving for retirement = $ 1,707,947.77**

**b) Calculation of Savings for retirement,if you wait
until age 39 to start saving**

Number of Annuity payments made = 65 - 39 = 26 years

FV = A((1+r)^n -1) / r

FV = 5000((1+0.11)^26 -1) / 0.11

FV = 5000(15.079865 -1) / 0.11

FV = 5000(14.079865) / 0.11

FV = 5000 * 127.998771

**FV = $ 639,993.86**

**Saving for retirement = $ 639,993.86**

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