Answer:
Please check the explanation.
Step-by-step explanation:
To find the amount we use the formula:
[tex]A=P\cdot \left(1+\frac{r}{n}\right)^{nt}[/tex]
Here:
A = total amount
P = principal or amount of money deposited,
r = annual interest rate
n = number of times compounded per year
t = time in years
Given
P=$2000
r=4.5%
n=4
t = 5 years
Calculating compounded quarterly
After plugging in the values
[tex]A=2000\left(1+\frac{4.5\%\:}{4}\right)^{4\cdot \:5}[/tex]
[tex]A=2000\left(1+\frac{0.045}{4}\right)^{4\cdot \:5}[/tex]
[tex]A=2000\cdot \frac{4.045^{20}}{4^{20}}[/tex]
[tex]A=\frac{125\cdot \:4.045^{20}}{2^{36}}[/tex]
[tex]A = 2,501.50[/tex]
Thus, If you deposit $2000 into an account paying 4.5% annual interest compounded quarterly, you will have $2501.50 after five years.
Calculating compounded semi-annually
n = 2
[tex]A=2000\left(1+\frac{4.5\%\:}{2}\right)^{2\cdot \:5}[/tex]
[tex]A=2000\left(1+\frac{0.045}{2}\right)^{2\cdot \:5}[/tex]
[tex]A=2000\cdot \frac{2.045^{10}}{2^{10}}[/tex]
[tex]A = 2,498.41[/tex]
Thus, If you deposit $2000 into an account paying 4.5% annual interest compounded semi-annually, you will have $2,498.41 after five years.
