Question

Twins graduate from college together and start their careers. Twin 1 invests $2000 at the end of each year for 10 years only (until age 33) in an account that earns 7%, compounded annually. Suppose that twin 2 waits until turning 40 to begin investing. How much must twin 2 put aside at the end of each year for the next 25 years in an account that earns 7% compounded annually in order to have the same amount as twin 1 at the end of these 25 years (when they turn 65)? (Round your answer to the nearest cent.)
$

Answer 1

Given Information:

As per data Current Age of twins is 23. Twin 1 Invested $2000 end of each year in coming 10 years till age 33.

Rate = 7%

1. Calculate the amount Twin 1 have at age 65. For this first calculate the amount she saved in 10 years.

FV at Year 10 = Annuity + Annuity x cumulative annuity factor @7% for 9 years.

[ For cumulative pv factor refer to your pv factor tables or you can calculate as it is sum of (1.07) + (1.07)² .....+(1.07)⁹ ]

FV = 2000 + ( 2000 x 12.81644795)

FV = 2000 + 25632.8959

Fv at Age 33= 27632.8959

Now calculate Fv at Age 65( after 32 years) with this lumpsum amount.

FV = PV(1+r)ⁿ

= 27632.8959 (1.07)³²

= 27632.8959 x 8.71527080

FV= 240828.1707

2. So $240828.1707 is the target amount for Twin 2 and She will start investing from Age 40. She has 25 years to accumulate this balance and she will deposit end of each year in this 25 years.

Calculate Annuity required to deposit for Twin 2

Fv = Annuity + Annuity x cumulative annuity factor @7% for 24 years.

240828.1707 = Annuity + Annuity x 62.24903749

240828.1707 = Annuity ( 1 + 62.24903749) [ taking Annuity common]

240828.1707 = Annuity x 63.24903749

Annuity = 240828.1707 / 63.24903749

Annuity = 3807.62 approx

Annual Contribution required $3807.62 to have the same balance as twin 1 have at Age 65.