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)?

show

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