you have $10,000 to invest and want to keep y...
you have $10,000 to invest and want to keep your money invested for 10 years. you are considering the following investment options. choose the investment option that will earn you the most money. a. 2.89% compounded monthly b. 2.975% compounded quarterly c. 2.99% compounded annually d. 3.25% simple interest please select the best answer from the choices provided a b c d
Answer
# Explanation:
## Step1: Recall compound - interest and simple - interest formulas
Compound - interest formula: $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Simple - interest formula: $A=P(1 + rt)$. Given $P = 10000$ and $t = 10$.
## Step2: Calculate the amount for option a
$r_a=0.0289$, $n_a = 12$.
$A_a=10000(1+\frac{0.0289}{12})^{12\times10}\approx10000(1 + 0.00240833)^{120}\approx10000\times1.3377\approx13377$.
## Step3: Calculate the amount for option b
$r_b = 0.02975$, $n_b=4$.
$A_b=10000(1+\frac{0.02975}{4})^{4\times10}=10000(1 + 0.0074375)^{40}\approx10000\times1.3494\approx13494$.
## Step4: Calculate the amount for option c
$r_c=0.0299$, $n_c = 1$.
$A_c=10000(1 + 0.0299)^{10}\approx10000\times1.3477\approx13477$.
## Step5: Calculate the amount for option d
$r_d=0.0325$.
$A_d=10000(1+0.0325\times10)=10000\times(1 + 0.325)=13250$.
# Answer:
B. 2.975% compounded quarterly