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Lan, who is self-employed, contributes $\$ 2000$ a month into a defined benefit retirement account earning interest at the rate of $r /$ year compounded monthly. At...

Question

Lan, who is self-employed, contributes $\$ 2000$ a month into a defined benefit retirement account earning interest at the rate of $r /$ year compounded monthly. At the end of 25 years, his account will be worth $$S=\frac{24,000\left[\left(1+\frac{r}{12}\right)^{300}-1\right]}{r}$$ dollars. a. Find the differential of $S$. b. Approximately how much more would lan's account be worth at the end of 25 years if his account earned 4.1\%/year instead of 4\%/year? 4.2\%/year instead of 4\%/year? 4

lan, who is self-employed, contributes $\$ 2000$ a month into a defined benefit retirement account earning interest at the rate of $r /$ year compounded monthly. At the end of 25 years, his account will be worth $$S=\frac{24,000\left[\left(1+\frac{r}{12}\right)^{300}-1\right]}{r}$$ dollars. a. Find the differential of $S$. b. Approximately how much more would lan's account be worth at the end of 25 years if his account earned 4.1\%/year instead of 4\%/year? 4.2\%/year instead of 4\%/year? 4.3\%/year instead of 4\%/year?



Answers

lan, who is self-employed, contributes $\$ 2000$ a month into a defined benefit retirement account earning interest at the rate of $r /$ year compounded monthly. At the end of 25 years, his account will be worth $$S=\frac{24,000\left[\left(1+\frac{r}{12}\right)^{300}-1\right]}{r}$$ dollars. a. Find the differential of $S$. b. Approximately how much more would lan's account be worth at the end of 25 years if his account earned 4.1\%/year instead of 4\%/year? 4.2\%/year instead of 4\%/year? 4.3\%/year instead of 4\%/year?


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