What is $600 invested at 9% interest, compounded quarterly, worth in 3 years?
a. $640.50
b. $641
c.$762
d.$784
amount = 600(1 + .09/4)^12
using:
Amount = principal(1+i)^n where i is the periodic interest rate of .09/4 and n is then number of interest periods, namely 12
To find the future value of an investment, we can use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- A is the future value (amount we are trying to find),
- P is the principal amount (initial investment),
- r is the annual interest rate (as a decimal),
- n is the number of times interest is compounded per year, and
- t is the number of years.
In this case, we have:
- P = $600 (principal amount),
- r = 9% or 0.09 (annual interest rate as a decimal),
- n = 4 (interest compounded quarterly), and
- t = 3 (3 years).
Now we can substitute these values into the formula and calculate the future value (A):
\[ A = 600 \left(1 + \frac{0.09}{4}\right)^{(4 \cdot 3)} \]
Now let's simplify this equation and find the value of A.