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 assume the full amount is withdrawn.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 $11052 (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: Identify the compound - interest formula

The compound - interest formula for monthly compounding 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. Here, $P=\$10000$, $r = 0.025$ (since $2.5\%=0.025$), $n = 12$ (monthly compounding), and $t = 4$.

Step2: Calculate the exponent

First, calculate $nt$. $nt=12\times4 = 48$.

Step3: Calculate the value inside the parentheses

Calculate $1+\frac{r}{n}=1+\frac{0.025}{12}\approx1 + 0.0020833=1.0020833$.

Step4: Calculate the compound - amount

Then, calculate $(1+\frac{r}{n})^{nt}=(1.0020833)^{48}$. Using a calculator, $(1.0020833)^{48}\approx1.10494$. Multiply by the principal: $A = 10000\times1.10494=\$11049$.

Answer:

$11049$