find the balance in the account after the given period. $5000 deposit earning 1.5% compounded quarterly…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years.

Step2: Convert the given values to the appropriate form

We have $P = 5000$, $r=0.015$ (since $1.5%=0.015$), $n = 4$ (compounded quarterly), and $t = 3$.

Step3: Substitute the values into the formula

$A=5000(1 +\frac{0.015}{4})^{4\times3}$. First, calculate the value inside the parentheses: $\frac{0.015}{4}=0.00375$, and $1+\frac{0.015}{4}=1 + 0.00375=1.00375$. Then, calculate the exponent: $4\times3 = 12$. So, $A = 5000\times(1.00375)^{12}$.

Step4: Calculate $(1.00375)^{12}$

Using a calculator, $(1.00375)^{12}\approx1.04585$.

Step5: Calculate the final amount $A$

$A = 5000\times1.04585=5229.25$.

Answer:

$5229.25$