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Chapter 8: Problem 22

You deposit \(\$ 12,000\) in an account that pays \(6.5 \%\) interest compounded quarterly. a. Find the future value after one year. b. Use the future value formula for simple interest to determine the effective annual yield.

Short Answer

Expert verified
The future value of the deposit after one year would be the value obtained at the end of step 1. The effective annual yield would be the percent value of r obtained in step 3.

Step by step solution

01

Calculate the future value (compound interest)

First, plug the given values into the future value formula for compound interest. Here, P = \(\$12,000\), i = \(6.5/100 = 0.065\), n = 4 (interest compounded quarterly) and t = 1 year. So, the formula becomes: \(FV = \$12000 * (1 + 0.065/4)^(4*1)\). Calculating this, one gets the future value.
02

Find the interest earned after one year

Next, find what will be the interest earned after one year. This can be obtained by subtracting the initial principal from the future value obtained in the first step.
03

Use the future value formula for simple interest to obtain the effective annual yield

Now, use the interest value obtained in the previous step to find the effective annual yield using the formula for simple interest: \(FV = P(1 + rt)\). Here, FV is the future value obtained in the first step, P is the initial principal, r is the rate we need to find, and t = 1 year. Rearranging the formula as \(r = (FV/P - 1)/t\), substitute the values and calculate r.

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