Suppose $3500 is invested in an account with an APR of 11% compounded monthly. Find the future value of the account in 3 years.
P = Po(1+r)^n.
Po = $3500.
r = (11% / 12) / 100% = 0.0091667 =
Monthly % rate expressed as a decimal.
n = 12Comp,/yr * 3yrs = 36 Compounding
periods.
Plug the above values into the given Eq
Answer: $4861.08.
To find the future value of the account in 3 years, we can use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
A is the future value of the account,
P is the principal amount (initial investment),
r is the annual interest rate (in decimal form),
n is the number of times interest is compounded per year, and
t is the number of years.
In this case, the principal amount (P) is $3500, the annual interest rate (r) is 11% or 0.11, the number of times interest is compounded per year (n) is 12 (since it's compounded monthly), and the number of years (t) is 3.
Substituting these values into the formula:
\[ A = 3500 \left(1 + \frac{0.11}{12}\right)^{(12)(3)} \]
We can simplify and calculate this expression to find the future value of the account.