Answer:
The total value of the investment will be $15,603.38 after 4 years
Step-by-step explanation:
Compound Interest
It occurs when interest in the next period is earned on the principal sum plus previously accumulated interest.
We'll use the formula:
[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]
Where:
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
The investment is P=$11,775 at a rate of r=7.10% = 0.071 compounded quarterly. Since there are 4 quarters in a year, n=4. The investment will last t=4 years, thus:
[tex]{\displaystyle A=\$11,775\left(1+{\frac {0.071}{4}}\right)^{4*4}}[/tex]
[tex]{\displaystyle A=\$11,775\left(1.01775\right)^{16}}[/tex]
[tex]\boxed{A = \$15,603.38}[/tex]
The total value of the investment will be $15,603.38 after 4 years
