Question

a bank offers the following two investment options. find the value for each investment option if $20,000 is invested for 10 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 assume the full amount is withdrawn.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. 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: Identify the compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, 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.

For the Long - Term Investment (CD)

The APY (Annual Percentage Yield) is given as $2.785\%=0.02785$. The formula for APY is $APY=(1 +\frac{r}{n})^{n}-1$. Since it's not clear if it's compounded monthly ($n = 12$) or other ways, but we can use the APY formula directly. Here, the principal $P=\$20000$, $t = 10$ years. The value of the investment $A$ is given by $A=P(1 + APY)^{t}$.
$A_{1}=20000\times(1 + 0.02785)^{10}$
$A_{1}=20000\times1.02785^{10}$
Using a calculator, $1.02785^{10}\approx1.3177$.
$A_{1}=20000\times1.3177=\$26354$

For the Money Maker Savings

The annual interest rate $r = 2.5\%=0.025$ and it is compounded monthly, so $n = 12$ and $t = 10$ years.
Using the compound - interest formula $A=P(1+\frac{r}{n})^{nt}$, we substitute $P = 20000$, $r=0.025$, $n = 12$, and $t = 10$.
$A_{2}=20000\times(1+\frac{0.025}{12})^{12\times10}$
First, calculate $\frac{0.025}{12}\approx0.0020833$.
Then $1+\frac{0.025}{12}=1.0020833$.
And $(1.0020833)^{120}\approx1.2833$.
$A_{2}=20000\times1.2833=\$25666$

Answer:

The value of the Long - Term Investment is $\$26354$, and the value of the Money Maker Savings is $\$25666$.