Given:
Principal (Investment) = $20,000
Interest Rate = 5.5% or 0.055 in decimal form
Time = 10 years
Compounding period = quarterly = 4 in every year
Find: the accrued amount or final amount after 10 years with interest
Solution:
To find the final amount after 10 years, we use the formula below.
[tex]F=P(1+\frac{r}{m})^{mt}[/tex]
where:
P = principal = $20,000
r = interest rate = 0.055
m = compounding period = 4
t = time = 10 years
Let's plug into the formula the values of each variable.
[tex]F=20,000(1+\frac{0.055}{4})^{4\times10}[/tex]
Solve for F.
a. Add the terms inside the parenthesis and multiply the exponents outside.
[tex]F=20,000(1.01375)^{40}[/tex]
b. Apply the exponent.
[tex]F=20,000(1.726770771)[/tex]
c. Multiply the two numbers.
[tex]\begin{gathered} F=34,535.41542 \\ F\approx34,535.42 \end{gathered}[/tex]
Answer:
After 10 years, there will be $34,535.42 available.
