## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 8 - Personal Finance - 8.4 Compound Interest - Exercise Set 8.4: 29

#### Answer

It is better to invest at a rate of 8% compounded monthly.

#### 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 money is invested at a rate of 8% compounded monthly. $Y = (1+\frac{r}{n})^{n}-1$ $Y = (1+\frac{0.08}{12})^{12}-1$ $Y = 0.0830$ The effective annual yield is 8.30% We can find the effective annual yield when money is invested at a rate of 8.25% compounded annually. $Y = (1+\frac{r}{n})^{n}-1$ $Y = (1+\frac{0.0825}{1})^{1}-1$ $Y = 0.0825$ The effective annual yield is 8.25% It is better to invest at a rate of 8% compounded monthly.

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