Question

 

Find the future value of the following ordinary annuities:

$600 per year for 10 years at 10%

$300 per year for 5 years at 5%

$600 per year for 5 years at 0%

Answer 1

Annuity is series of equal cash flows for certain period of time, if periodic cash flow is P, number of period is n, and interest per period is r then future value of cash flow will be

FV of annuity = P [(1 + r)^n - 1]/ r

Let's put the values in the formula,

= 600[(1 + 0.1)^10 - 1]/ 0.1

= 600[(1.1 )^10 - 1]/ 0.1

= 600 ( 2.5937424601 ) - 1/ 0.1

= 600 ( 1.5937424601 )/ 0.1

= 600 * 15.937424601

= 9562.45

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FV of annuity = P [(1 + r)^n - 1]/ r

Let's put the values in the formula,

= 300[(1 + 0.05)^5 - 1]/ 0.05

= 300[(1.05 )^5 - 1]/ 0.05

= 300 ( 1.2762815625 ) - 1/ 0.05

= 300 ( 0.2762815625 )/ 0.05

= 300 * 5.52563125

= 1657.69

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If the interest rate is 0 then FV of annuity will be

FV = 600* 5 = 3000

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