Question

# You are 30 years old and decide to start saving for your retirement. You plan to...

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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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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