Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 8 - Personal Finance - 8.4 Compound Interest - Exercise Set 8.4: 32

Answer

It is better to invest at a rate of 6.85% compounded daily.

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 7% compounded annually. $Y = (1+\frac{r}{n})^{n}-1$ $Y = (1+\frac{0.07}{1})^{1}-1$ $Y = 0.07$ The effective annual yield is 7.0% We can find the effective annual yield when money is invested at a rate of 6.85% compounded daily. $Y = (1+\frac{r}{n})^{n}-1$ $Y = (1+\frac{0.0685}{360})^{360}-1$ $Y = 0.0709$ The effective annual yield is 7.1% It is better to invest at a rate of 6.85% compounded daily.
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