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Problem 12

# Calculate the present value of an investment that will be worth $$\ 1,000$$ at the stated interest rate after the stated amount of time. 10 years, at $$5.3 \%$$ per year, compounded quarterly

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## Step 2: Convert the annual interest rate to a decimal

To convert the annual interest rate to a decimal, divide the percentage by 100. r = $$5.3 \% = \frac{5.3}{100} = 0.053$$

## Step 3: Calculate the total number of periods

To calculate the total number of periods, multiply the time in years (t) by the compounding frequency (n). Total number of periods (p) = $$t \times n$$ p = $$10 \times 4 = 40$$

## Step 4: Calculate the effective interest rate per period

Now, divide the annual interest rate (r) by the compounding frequency (n) to get the effective interest rate per period. Interest rate per period (i) = $$\frac{r}{n}$$ i = $$\frac{0.053}{4} = 0.01325$$

## Step 5: Calculate the present value

Now, use the present value formula to calculate the present value. PV = $$\frac{FV}{(1+i)^p}$$ PV = $$\frac{1000}{(1+0.01325)^{40}}$$ PV ≈ $$563.50$$ The present value of the investment is approximately $$\563.50$$.

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