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 assume the full amount is withdrawn.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 + r/12)^12 - 1. early withdrawal fee before 10 years is 2% of account balance. (round to the nearest dollar as needed.) the value of the long - term investment is $ . 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 money maker savings is $

Explanation:

Step1: Identify the compound - interest formula for Money Maker Savings

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 Money Maker Savings, $P=\$10000$, $r = 0.025$, $n = 12$, and $t = 4$.

Step2: Substitute the values into the formula

$A=10000(1 +\frac{0.025}{12})^{12\times4}$.
First, calculate the value inside the parentheses: $\frac{0.025}{12}\approx0.0020833$, then $1+\frac{0.025}{12}=1 + 0.0020833=1.0020833$.
Next, calculate the exponent: $12\times4 = 48$.
So, $A = 10000\times(1.0020833)^{48}$.

Step3: Calculate $(1.0020833)^{48}$

Using a calculator, $(1.0020833)^{48}\approx1.105167$.

Step4: Calculate the final amount $A$

$A=10000\times1.105167=\$11052$ (rounded to the nearest dollar).

For the 10 - year CD, since we are not asked to calculate its value based on the APY formula given ($APY=(1 +\frac{r}{12})^{12}-1$) and only need the Money Maker Savings value, we focus on the above - calculated result.

Answer:

$11052$