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 assume the full amount is withdrawn.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!
high apy!
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 $\square$, and the value of the money maker savings is $\square$. (round to the nearest dollar as needed.)

Explanation:

Step1: Calculate the value of the Long - Term Investment (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 with an APY (Annual Percentage Yield) of $2.785\%=0.02785$, and $P = 10000$, $n = 10$.
$A_{CD}=10000\times(1 + 0.02785)^{10}$
$A_{CD}=10000\times1.02785^{10}\approx10000\times1.32197\approx13220$

Step2: Calculate the value of the Money Maker Savings

The initial interest rate $r_1=2.5\% = 0.025$, compounded monthly ($m = 12$). For the first 4 - year period, $n_1 = 4$, $P = 10000$. The compound - interest formula is $A=P(1+\frac{r}{m})^{mn}$.
$A_1=10000\times(1+\frac{0.025}{12})^{12\times4}$
$A_1=10000\times(1+\frac{0.025}{12})^{48}\approx10000\times1.10494\approx11049$

For the next 4 - year period, the interest rate increases by $0.25\%$, so $r_2=2.5\%+0.25\% = 2.75\%=0.0275$, and $P = A_1\approx11049$, $n_2 = 4$.
$A_2=11049\times(1+\frac{0.0275}{12})^{12\times4}$
$A_2=11049\times(1+\frac{0.0275}{12})^{48}\approx11049\times1.11727\approx12345$

Answer:

The value of the Long - Term Investment is $\$13220$, and the value of the Money Maker Savings is $\$12345$