Question

a bank offers the following two investment options. find the value for each investment option if $20,000 is invested for 8 years. assume the full amount is withdrawn. long - term investment! high apr! 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 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, $P=\$20000$, the APY $r = 0.02785$, and $n = 10$.
$A_{CD}=20000\times(1 + 0.02785)^{10}$
$A_{CD}=20000\times1.02785^{10}$
Using a calculator, $1.02785^{10}\approx1.3117$.
$A_{CD}=20000\times1.3117=\$26234$

Step2: Calculate the value of the Money - Maker Savings

The initial interest rate $r_0=0.025$, and the interest is compounded monthly, so $m = 12$. The number of years $n = 8$.
The compound - interest formula for monthly compounding is $A=P(1+\frac{r}{m})^{mn}$.
For the first 4 years:
$A_1 = 20000\times(1+\frac{0.025}{12})^{12\times4}$
$A_1 = 20000\times(1+\frac{0.025}{12})^{48}$
Using a calculator, $(1+\frac{0.025}{12})^{48}\approx1.1049$.
$A_1 = 20000\times1.1049=\$22098$

After 4 years, the interest rate increases by $0.25\%$, so the new interest rate $r_1=0.025 + 0.0025=0.0275$.
For the next 4 years:
$A_2=A_1\times(1+\frac{0.0275}{12})^{12\times4}$
$A_2 = 22098\times(1+\frac{0.0275}{12})^{48}$
Using a calculator, $(1+\frac{0.0275}{12})^{48}\approx1.1177$.
$A_2=22098\times1.1177=\$24609$

Answer:

The value of the Long - Term Investment (10 - year CD) is $\$26234$, and the value of the Money Maker Savings is $\$24609$