Question

You deposit $5,000 in the bank each year starting today.

The last deposit will be in exactly 20 years’ time.

How much will there be in the bank when you retire in exactly 45 years?

EAR = 10%

Answer 1

FV of Annuity Due:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here deposits are made at the begining of the period. FV of annuity is future value of cash flows deposited at regular intervals grown at specified int rate or Growth rate to future date.

FV of Annuity DUe = ( 1 + r ) * FV of Annuity

FV of Annuity = (1+r) * CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

Amount at the end of 21Years:

Particulars	Amount
Cash Flow	$      5,000.00
Int Rate	10.000%
Periods	21

FV of Annuity Due = ( 1+ r) [ Cash Flow * [ [ ( 1 + r )^n ] - 1 ] /r ]
= ( 1 + 0.1 ) * [5000 * [ [(1+0.1)^21] - 1 ] / 0.1 ]
= ( 1.1 ) * [5000 * [ [( 1.1 ) ^ 21 ] - 1 ] / 0.1 ]
= ( 1.1 ) * [5000 * [ [ 7.4002 ] - 1 ] / 0.1 ]
= ( 1.1 ) * [ $ 320012.5 ]
= $ 352013.75

Future Value after 45 Years:

Particulars	Amount
Present Value	$       352,013.75
Int Rate	10.0000%
Periods	24

Future Value = Present Value * ( 1 + r )^n
= $ 352013.75 ( 1 + 0.1) ^ 24
= $ 352013.75 ( 1.1 ^ 24)
= $ 352013.75 * 9.8497
= $ 3467241.34

Value in account after 45 Years is $ 3,467,241.34