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Problem 10

# Find the present value of each ordinary annuity. $$\ 1200 /$$ semiannual period for 6 yr at $$10 \%$$ lyear compounded semiannually

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The formula for the present value of an ordinary annuity is: $PV = PMT * \frac{1 - (1 + r)^{-n}}{r}$ Plugging in the variables: - PMT: $1200 - r: 0.05 - n: 12 ## Step 3: Calculate the present value Using the formula from Step 2 and plugging in the variables, we get: $PV = 1200 * \frac{1 - (1 + 0.05)^{-12}}{0.05}$ First, we'll calculate the expression inside the parentheses: $(1 + 0.05)^{-12} \approx 0.5403$ Now, subtract this from 1 and divide by the interest rate: $\frac{1 - 0.5403}{0.05} \approx 9.194$ Finally, multiply by the payment per period: $PV = 1200 * 9.194 \approx 11032.8$ Therefore, the present value of this ordinary annuity is approximately$11032.8.

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