## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 8 - Personal Finance - 8.4 Compound Interest - Exercise Set 8.4 - Page 522: 57

#### Answer

The account paying 4.5% interest compounded semiannually is a better investment.

#### Work Step by Step

This is the formula we use when we find the effective annual yield $Y$: $Y = (1+\frac{r}{n})^{n}-1$ $Y$ is the effective annual yield $r$ is the stated interest rate $n$ is the number of times per year the interest is compounded We can find the effective annual yield when the 4.5% interest is compounded semiannually. $Y = (1+\frac{r}{n})^{n}-1$ $Y = (1+\frac{0.045}{2})^{2}-1$ $Y = 0.0455$ The effective annual yield is 4.55% We can find the effective annual yield when the 4.4% interest is compounded daily. $Y = (1+\frac{r}{n})^{n}-1$ $Y = (1+\frac{0.044}{360})^{360}-1$ $Y = 0.0450$ The effective annual yield is 4.50% The account paying 4.5% interest compounded semiannually is a better investment.

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