Suppose that $5000 is invested in an account with an account with an APR of 12% compounded monthly. Find the future value of the account in 5 years.
To find the future value of the account, 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 investment
- P is the principal amount (initial investment), which is $5000 in this case
- r is the annual interest rate as a decimal, which is 12% or 0.12
- n is the number of compounding periods per year, which is 12 in this case (monthly compounding)
- t is the number of years, which is 5 in this case
By substituting the given values into the formula, we can calculate the future value of the account:
\[A = 5000 \left(1 + \frac{0.12}{12}\right)^{(12)(5)}\]
Now, let's compute the expression inside the parentheses first:
\[1 + \frac{0.12}{12} = 1 + 0.01 = 1.01\]
Next, let's evaluate the exponent:
\((12)(5) = 60\)
Now, we can substitute these values back into the formula and calculate the future value of the account:
\[A = 5000 (1.01)^{60}\]
Using a calculator, we find that
\[A \approx 7938.84\]
Therefore, the future value of the account after 5 years will be approximately $7938.84.