Question

a bank offers the following two investment options. find the value for each investment option if $10,000 is invested for 4 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 assume the full amount is withdrawn.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 + \\(\frac{r}{12}\\))^12 - 1. early withdrawal fee before 10 years is 2% of account balance.
the value of the long - term investment is $ and the value of the money maker savings is $ (round to the nearest dollar as needed.)
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%!

Explanation:

Step1: Calculate the value of the 10 - year CD

The formula for compound - interest is $A = P(1 + r)^n$, where $P$ is the principal amount, $r$ is the annual interest rate, and $n$ is the number of years. For the 10 - year CD, the APY (Annual Percentage Yield) $r=0.02785$ and $P = 10000$, $n = 10$.
$A_{CD}=10000\times(1 + 0.02785)^{10}$
$A_{CD}=10000\times1.02785^{10}$
Using a calculator, $1.02785^{10}\approx1.32177$.
$A_{CD}=10000\times1.32177 = 13218$ (rounded to the nearest dollar)

Step2: Calculate the value of the Money Maker Savings

The initial interest rate $r_0=0.025$. After 4 years, the interest rate increases by $0.0025$, so the new interest rate $r_1=0.025 + 0.0025=0.0275$.
The compound - interest formula for monthly compounding is $A=P(1+\frac{r}{m})^{mn}$, where $m = 12$ (number of compounding periods per year), $P = 10000$, for the first 4 years $r = 0.025$ and $n = 4$, and for the remaining $0$ years with the new rate (since the investment is for 4 years), we first calculate the amount after 4 years with the initial rate.
$A_{1}=10000\times(1+\frac{0.025}{12})^{12\times4}$
Let $x=\frac{0.025}{12}\approx0.0020833$ and $y = 12\times4 = 48$. Then $(1 + x)^y=(1+0.0020833)^{48}$.
Using a calculator, $(1 + 0.0020833)^{48}\approx1.10516$.
$A_{1}=10000\times1.10516=11052$ (rounded to the nearest dollar)

Answer:

The value of the Long - Term Investment (10 - year CD) is $\$13218$ and the value of the Money Maker Savings is $\$11052$