# Chapter 8 - Personal Finance - 8.4 Compound Interest - Exercise Set 8.4: 21

(a) After 1 year, there will be \$10,457.65 in the account. (b) The effective annual yield is 4.5765% #### Work Step by Step (a) This is the formula we use when we make calculations with compound interest:$A = P~(1+\frac{r}{n})^{nt}A$is the final amount in the account$P$is the principal (the amount of money invested)$r$is the interest rate$n$is the number of times per year the interest is compounded$t$is the number of years$A = P~(1+\frac{r}{n})^{nt}A = (\$10,000)~(1+\frac{0.045}{4})^{(4)(1)}$ $A = \$10,457.65$After 1 year, there will be \$10,457.65 in the account. (b) This is the formula we use when we make calculations with simple interest: $A = P~(1+rt)$ $1+rt = \frac{A}{P}$ $r = \frac{\frac{A}{P}-1}{t}$ $r = \frac{\frac{\$10,457.65}{\$10,000}-1}{1}$ $r = 0.045765$ The effective annual yield is 4.5765%

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