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Problem 10

# Find the present value of the given investment. An investment earns $$10 \%$$ per year and is worth $$\ 5,000$$ after 3 months.

Expert verified
The present value of the given investment is approximately $4,878.13, when considering a 10% annual interest rate and a future value of$5,000 after 3 months.
See the step by step solution

## Step 1: Recall or provide the formula for present value.

The formula for calculating the present value (PV) of an investment is given by: $PV = \frac{FV}{(1 + r)^n}$ where $$FV$$ is the future value, $$r$$ is the interest rate per period, and $$n$$ is the number of periods.

In this problem, we are given an annual interest rate of 10%, which needs to be converted into a monthly interest rate. We can do this by dividing the annual interest rate by 12, as there are 12 months in a year. So the monthly interest rate is: $$r=\frac{10\%}{12} \approx 0.008333$$ Also, the given investment is worth $5,000 after 3 months, so the number of periods $$n = 3$$. ## Step 3: Use the present value formula and the values obtained in the previous step to calculate the present value of the given investment. Now we can plug in our values for $$FV$$, $$r$$, and $$n$$ into the present value formula: $PV = \frac{5,000}{(1 + 0.008333)^3}$ Calculating the denominator: $$(1 + 0.008333)^3 \approx 1.0251$$ Now dividing$5,000 by the denominator: $PV = \frac{5,000}{1.0251} \approx 4,878.13$ The present value of the given investment is approximately \$4,878.13.

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