What is the future value of an ordinary annuity with PMT = 100 for n = 3 at i = 5%?

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Multiple Choice

What is the future value of an ordinary annuity with PMT = 100 for n = 3 at i = 5%?

Explanation:
Understanding how to find the future value of an ordinary annuity requires applying the future value formula for end-of-period payments: FV = PMT × [((1 + i)^n − 1) / i]. With a periodic payment of 100, a rate of 5% per period, and 3 periods, compute (1.05)^3 = 1.157625. Subtract 1 to get 0.157625, divide by 0.05 to get 3.1525, and multiply by 100 to obtain 315.25. Thus the future value after three payments is 315.25. This makes sense because the payments earn interest according to when they’re paid: the first payment grows for two periods, the second for one period, and the last for zero periods, giving 100×1.05^2 + 100×1.05 + 100 = 110.25 + 105 + 100 = 315.25.

Understanding how to find the future value of an ordinary annuity requires applying the future value formula for end-of-period payments: FV = PMT × [((1 + i)^n − 1) / i]. With a periodic payment of 100, a rate of 5% per period, and 3 periods, compute (1.05)^3 = 1.157625. Subtract 1 to get 0.157625, divide by 0.05 to get 3.1525, and multiply by 100 to obtain 315.25. Thus the future value after three payments is 315.25. This makes sense because the payments earn interest according to when they’re paid: the first payment grows for two periods, the second for one period, and the last for zero periods, giving 100×1.05^2 + 100×1.05 + 100 = 110.25 + 105 + 100 = 315.25.

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