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Gabrielle purchased an annuity that had an interest rate of 3.50% compounded semi-annually. It provided her...

Gabrielle purchased an annuity that had an interest rate of 3.50% compounded semi-annually. It provided her with payments of $1,000 at the end of every month for 7 years. If the first withdrawal is to be made in 5 years and 1 month, how much did she pay for it?

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Answer #1

Effective monthly rate, r = (1 + 0.035/2)^(1/6) - 1

r = 0.002895623966

n = 7 * 12 = 84

Now, with this as FV, let's find the value today.

Effective annual rate, r = (1 + 0.035/2)^2 - 1

r = 0.03530625

PV = FV/(1 + r)^n

PV = 74,469.3044511153/(1 + 0.03530625)^5

PV = $62,608.473999264

Gabrielle paid $62,608.473999264 for the annuity

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