## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 8 - Personal Finance - 8.4 Compound Interest - Exercise Set 8.4: 58

#### Answer

The account paying 4.9% 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 4.9% interest is compounded semiannually. $Y = (1+\frac{r}{n})^{n}-1$ $Y = (1+\frac{0.049}{2})^{2}-1$ $Y = 0.0496$ The effective annual yield is 4.96% We can find the effective annual yield when the 4.8% interest is compounded daily. $Y = (1+\frac{r}{n})^{n}-1$ $Y = (1+\frac{0.048}{360})^{360}-1$ $Y = 0.0492$ The effective annual yield is 4.92% The account paying 4.9% interest compounded semiannually is a better investment.

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