9. you deposit $1600 in a bank account. find the balance after 3 years for each of the following situations…

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. Given $P = 1600$, $t = 3$.

Step2: Solve part a

For part a, $r=0.025$ (since $2.5%=0.025$) and $n = 12$ (compounded monthly). $A=1600(1 +\frac{0.025}{12})^{12\times3}$ $A=1600(1+\frac{0.025}{12})^{36}$ $A\approx1600(1 + 0.0020833)^{36}$ $A\approx1600\times1.07788$ $A\approx1724.61$

Step3: Solve part b

For part b, $r = 0.0175$ (since $1.75%=0.0175$) and $n = 4$ (compounded quarterly). $A=1600(1+\frac{0.0175}{4})^{4\times3}$ $A=1600(1 + 0.004375)^{12}$ $A\approx1600\times1.05388$ $A\approx1686.21$

Step4: Solve part c

For part c, $r = 0.04$ (since $4%=0.04$) and $n = 1$ (compounded yearly). $A=1600(1+\frac{0.04}{1})^{1\times3}$ $A=1600(1.04)^{3}$ $A=1600\times1.124864$ $A\approx1799.78$

Answer:

a. $$1724.61$ b. $$1686.21$ c. $$1799.78$