# Chapter 8 - Sequences, Induction, and Probability - Exercise Set 8.3 - Page 741: 77

a). Amount saved after 5 year A= 11,616.8 b). Interest = 1,616.8

#### Work Step by Step

a). Deposit on first year $a_{1}$ = 2000 Compound interest rate is 7.5% = 0.075 Amount saved after n year A = $\frac{P [(1 + \frac{r}{n})^{n\times t} - 1]}{\frac{r}{n}}$ Amount saved after 5 year A = $\frac{2000 [(1 + \frac{0.075}{1})^{1\times 5} - 1]}{\frac{0.075}{1}}$ = $\frac{2000 [(1 + 0.075)^{5} - 1]}{0.075}$ = $\frac{2000 [(0.4356]}{0.075}$ = 2000 $\times$ 5.8= 11616.8 b). Interest = 11616.8 - (2000$\times$5) = 11616.8 - 10000 = 1616.8

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