Question

Susan saved $5000 per year in her retirement account for 10 years (during age 25-35) and then quit saving. However, she did not make any withdrawal until she turned 65 (i.e., 30 years after she stopped saving). Her twin sister, Jane did not save anything during the 1st 10 years (during age 25-30) but saved $5,000 per year for 30 years (during age 35-65). What will be the difference in their retirement account balance at age 65, if their investments earned an average return of 8.5% during the entire period?

Answer 1

Retirement balance of susen calculation :

FV of Annuity :
Annuity is series of cash flows that are deposited at regular intervals for specific period of time.
FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per Year
n - No. of Year

Particulars	Amount
Cash Flow	$      5,000.00
Int Rate	8.500%
Periods	10

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 5000 * [ [ ( 1 + 0.085 ) ^ 10 ] - 1 ] / 0.085
= $ 5000 * [ [ ( 1.085 ) ^ 10 ] - 1 ] / 0.085
= $ 5000 * [ [2.261] - 1 ] / 0.085
= $ 5000 * [1.261] /0.085
= $ 74175.5

Future Value of $ 74175.5 deposited for 30 years @8.5% per annum

Future Value:

FV = PV (1+r)^n

Where r is Int rate per Year

n - No. of Year

Future Value Calculation:
Particulars	Amount
Present Value	$                       74,175.50
Int Rate	8.5000%
Periods	30

Future Value = Present Value * ( 1 + r )^n
= $ 74175.5 ( 1 + 0.085) ^ 30
= $ 74175.5 ( 1.085 ^ 30)
= $ 74175.5 * 11.5583
= $ 857339.09

Jane retirement balance calculation :

FV of Annuity
Particulars	Amount
Cash Flow	$      5,000.00
Int Rate	8.500%
Periods	30

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 5000 * [ [ ( 1 + 0.085 ) ^ 30 ] - 1 ] / 0.085
= $ 5000 * [ [ ( 1.085 ) ^ 30 ] - 1 ] / 0.085
= $ 5000 * [ [11.5583] - 1 ] / 0.085
= $ 5000 * [10.5583] /0.085
= $ 621073.63

Difference in retirement balances at age 65 = Balance of susen - Balance of jane

=  $ 857339.09 - $ 621073.63

= $ 236265.46