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Chapter 8: Problem 21

You deposit \(\$ 10,000\) in an account that pays \(4.5 \%\) 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
a. The future value after one year will be approximately \$10,454.60. b. The effective annual yield will be approximately 4.546%

Step by step solution

01

Identifying Given Constants

The exercise has given a principal amount of \$10,000, an interest rate of 4.5% compounded quarterly and a time period of 1 year. For quarterly compounding, the compounding periods (n) in one year are 4.
02

Calculating Future Value

We can now use the future value formula for compound interest to calculate this: \(FV = P (1 + r/n) ^{nt}\). Substituting the given values, we have \(FV = \$10,000 (1 + 0.045/4) ^{(4*1)} = \$10,454.60\). So the future value after one year will be \$10,454.60.
03

Calculating the Effective Annual Yield

The effective annual yield can be calculated using the future value formula for simple interest which is \(FV = P + P*r*t\) . Rearranging the formula for the yield (r), we get \(r = (FV - P) / (P*t)\). Substituting the values, we get \(r = (\$10,454.60-\$10,000) / (\$10,000*1) = 0.04546\). Converting this to percentage, we get approx. 4.546% annual yield.

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