Question

a bank offers the following two investment options. find the value for each investment option if $10,000 is invested for 5 years. assume the full amount is withdrawn. long - term investment! 10 - year cd at 2.785% apy! apply online or at one of our convenient locations! note: cd means certificate of deposit. apy=(1 + \LXI0)^{12}-1. early withdrawal fee before 10 years is 2% of account balance. money maker savings! minimum balance: $10,000. earn 2.5% interest compounded monthly. loyalty program! every 4 years with us, your interest rate increases by 0.25%! the value of the long - term investment is $□, and the value of the money maker savings is $□. (round to the nearest dollar as needed.)

Explanation:

Step1: Calculate the future - value of the Long - Term Investment (CD)

The formula for the future value $A$ of an investment with annual percentage yield (APY) is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the APY, and $t$ is the number of years. Here, $P=\$10000$, $r = 0.02785$ (2.785% APY), and $t = 10$.
$A_{CD}=10000\times(1 + 0.02785)^{10}$
$A_{CD}=10000\times1.02785^{10}$
Using a calculator, $1.02785^{10}\approx1.32197$. So, $A_{CD}=10000\times1.32197=\$13220$ (rounded to the nearest dollar).

Step2: Calculate the future - value of the Money Maker Savings

The formula for compound interest is $A=P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate, $n$ is the number of times interest is compounded per year, and $t$ is the number of years.
The initial interest rate $r_1 = 0.025$. Since there are no 4 - year intervals in 5 years, the interest rate remains $r = 0.025$, $n = 12$ (compounded monthly), $P=\$10000$, and $t = 5$.
$A_{savings}=10000\times(1+\frac{0.025}{12})^{12\times5}$
$A_{savings}=10000\times(1+\frac{0.025}{12})^{60}$
First, calculate $1+\frac{0.025}{12}\approx1.0020833$. Then, $(1.0020833)^{60}\approx1.132707$. So, $A_{savings}=10000\times1.132707=\$11327$ (rounded to the nearest dollar).

Answer:

The value of the Long - Term Investment is $\$13220$, and the value of the Money Maker Savings is $\$11327$.