Question

Find the value of the ordinary annuity at the end of the indicated time period. The payment​ R, frequency of deposits m​ (which is the same as the frequency of​ compounding), annual interest rate​ r, and time t are given below.

​Amount, ​$700​; ​monthly; 3​%; 3 years

Answer 1

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)^m - 1 ] / r
r - Int rate per period = r/no. of compounding per year = 3% / 12 = 0.25 % or 0.0025
m - No. of periods = 3 yaers * 12 = 36

Particulars	Amount
Cash Flow	$                700.00
Int Rate	0.2500%
Periods	36

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 700 * [ [ ( 1 + 0.0025 ) ^ 36 ] - 1 ] / 0.0025
= $ 700 * [ [ ( 1.0025 ) ^ 36 ] - 1 ] / 0.0025
= $ 700 * [ [1.0941] - 1 ] / 0.0025
= $ 700 * [0.0941] /0.0025
= $ 26334.39

Value of the ordinary annuity at the end of the period = $ 26334.39

answered by: anonymous