Question

Susan and Kim are twin sisters. Susan starts investing $100 a month at age 25 and invests for 10 years 35 at 5% compounded monthly. Susan stops investing at age 35, and does not contribute any money for the next 30 years. Kim starts investing at age 30, $150 a month at 5% for 30 years. Now at age 65:

a) How much money has Susan deposited?

b) How much money has Kim deposited?

c) Who has saved the most money? be sure to give the totals for both sisters

Answer 1

The interest rate is 5% compounded monthly.
FV = PMT * (1+Interest Rate)^Duration

FV of an annuity = P * ((1+r)ⁿ - 1) / r

a) Susan has deposited $100 per month for 10 years.
100 * 120 = 12000
Susan has deposited a total of $12000 in the ten years.

=FV(5%/12,120,-100,,0)
= 15528.23

b) Kim deposited $150 per month for 30 years.
150 * ( 30 * 12 ) = 54000

Kim has deposited a total of $54000

=FV(5%/12,360,-150,,0)
= 124838.80

c) The future worth of Susan
We will use FV of annuity formula

100 * (( 1.0042 )¹²⁰ - 1 )/( 0.0042 )
= 100 * (1.6536 - 1 ) / 0.0042
= 100 * 155.6150
= 15561.50

If the above amount generated returns up to next 30 years
15561.50 * ( 1.0042 )³⁰⁰
= 15561.50 * 3.5161
= 54716.28

The future worth of Kim
We will use FV of annuity formula

150 * ((1.0042)³⁶⁰ -1 ) / 0.0042
= 150 * ( 4.5214 - 1 ) / 0.0042
= 150 * 838.4415
= 125766.22

Kim has a longer series cash flow deposits than Susan, so she had a higher value of her savings.

Please note that some numbers will vary because of rounding off.