Monthly payments of 100 are paid into an annuity beginning o

Monthly payments of $100 are paid into an annuity beginning on January? 31, with a yearly interest rate of 3 percent, compounded monthly. Add the future values of each payment to calculate the total value of the annuity on September 1.

Solution

Future value on 1 Sep = $807.04

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Interest rate per month = 3/12 = 0.25% per month

Time = 8 months

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,

= 100[(1 + 0.0025)^8 - 1]/ 0.0025

= 100[(1.0025) ^8 - 1]/ 0.0025

= 100 (1.0201758777) - 1/ 0.0025

= 100 (0.0201758777000001)/ 0.0025

= 100 * 8.07035108000003

= 807.04

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