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 assume the full amount is withdrawn.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 APY formula is $APY=(1 +\frac{r}{12})^{12}-1$, where $r$ is the annual interest rate. For the 10 - year CD with an APY of $2.785\%=0.02785$.
The compound - interest formula is $A = P(1 + r)^{t}$, but since we have APY, for a 10 - year investment with $P=\$10000$, the value $A_1$ of the 10 - year CD after 10 years is $A_1=10000(1 + 0.02785)^{10}$.
\[A_1=10000\times1.02785^{10}\approx10000\times1.32709\approx13271\]

Step2: Calculate the value of the Money Maker Savings

The annual interest rate $r = 2.5\%=0.025$. For a 4 - year investment with monthly compounding ($n = 12$), the compound - interest formula is $A=P(1+\frac{r}{n})^{nt}$, where $P = 10000$, $n = 12$, $t = 4$.
\[A_2=10000(1+\frac{0.025}{12})^{12\times4}=10000(1+\frac{0.025}{12})^{48}\]
\[1+\frac{0.025}{12}\approx1 + 0.0020833=1.0020833\]
\[A_2=10000\times1.0020833^{48}\approx10000\times1.10494\approx11049\]

Answer:

The value of the Long - Term Investment (10 - year CD) is $\$13271$ and the value of the Money Maker Savings is $\$11049$