Question

Suppose that you deposit $871 in a savings account at Prosperity Bank at the end of each of the next 7 months. You plan to leave these contributions and any interest earned in the account until 7 months are up. The interest rate is 2.47% per month. What is the future value of your account at the end of the holding period? Do not round at intermediate steps in your calculation. Round your final answer to the nearest penny. Do not type the $ symbol.

Answer 1

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	$               871.00
Int Rate	2.470%
Periods	7

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 871 * [ [ ( 1 + 0.0247 ) ^ 7 ] - 1 ] / 0.0247
= $ 871 * [ [ ( 1.0247 ) ^ 7 ] - 1 ] / 0.0247
= $ 871 * [ [1.1863] - 1 ] / 0.0247
= $ 871 * [0.1863] /0.0247
= $ 6567.85
Amount in Account after 7 Months is $ 6567.85