# Chapter 8 - Personal Finance - 8.4 Compound Interest - Exercise Set 8.4: 31

It is better to invest at a rate of 5.5% compounded semiannually.

#### 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 5.5% compounded semiannually. $Y = (1+\frac{r}{n})^{n}-1$ $Y = (1+\frac{0.055}{2})^{2}-1$ $Y = 0.05576$ The effective annual yield is 5.58% We can find the effective annual yield when money is invested at a rate of 5.4% compounded daily. $Y = (1+\frac{r}{n})^{n}-1$ $Y = (1+\frac{0.054}{360})^{360}-1$ $Y = 0.0555$ The effective annual yield is 5.55% It is better to invest at a rate of 5.5% compounded semiannually.

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