Question

What's the future value of a 3%, 5-year ordinary annuity that pays $200 each year? If this was an annuity due, what would its future value be? Do not round intermediate calculations. Round your answers to the nearest cent.

Future Value of an Ordinary Annuity: $  

Future Value of an Annuity Due: $  

Answer 1

Part A:

FV of Annuity :

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here deposits are made at the end 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 = CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$               200.00
Int Rate	3.000%
Periods	5

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 200 * [ [ ( 1 + 0.03 ) ^ 5 ] - 1 ] / 0.03
= $ 200 * [ [ ( 1.03 ) ^ 5 ] - 1 ] / 0.03
= $ 200 * [ [1.1593] - 1 ] / 0.03
= $ 200 * [0.1593] /0.03
= $ 1061.83

Part B:

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

Particulars	Amount
Cash Flow	$         200.00
Int Rate	3.000%
Periods	5

FV of Annuity Due = ( 1+ r) [ Cash Flow * [ [ ( 1 + r )^n ] - 1 ] /r ]
= ( 1 + 0.03 ) * [200 * [ [(1+0.03)^5] - 1 ] / 0.03 ]
= ( 1.03 ) * [200 * [ [( 1.03 ) ^ 5 ] - 1 ] / 0.03 ]
= ( 1.03 ) * [200 * [ [ 1.1593 ] - 1 ] / 0.03 ]
= ( 1.03 ) * [ $ 1061.83 ]
= $ 1093.68

Pls comment, if any further assistance is required.