How much will Sam make after 8 years if she earns 12% compound annuity and invests $200 at the beginning of every year?

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FVA Continuous Compounding = Cash Flow * [(ert -1)/ (er -1)]

FVA = Future Value of Annuity

r = rate per period

t = time in months

OR

FVAD = C *[{(1+r)t -1}/r] * (1+r)

FVAD = Future Value of Annuities Due

C = Cash flows

r = rate per period

t = time equivalent to the number of payment periods

Applying this to your question,

Cash Flow = $200

r = 12% annual rate

t = 8 years, equivalent to 8 periods

$200 * [((1.12)(8) -1)/0.12]*(1+0.12) = $2755.13

The future value of annuities due is a slight modification of the future value of ordinary annuities because of the nature of cash flows. For the future value of annuities due, 1 is added to the rate and multiplied by the future value of ordinary annuities equation to compensate for the cash flow timings. Thus, the future value of ordinary annuities does not include the last part of the FVAD equation (* 1+r).

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