Carly deposits $900 into an annuity at the end of every month for 2.5 years. The fund holds international stocks, and it yields about 12% compounded monthly. Find the interest earned after 2.5 years.
To find the interest earned after 2.5 years, we need to first calculate the total amount of money accumulated in the annuity over this period.
Let's break down the given information:
- Carly deposits $900 at the end of every month.
- The annuity is held for 2.5 years, which means there are 2.5 x 12 = 30 monthly deposits.
- The fund yields 12% compounded monthly.
To calculate the future value of the annuity, we can use the formula for compound interest:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = future value (total amount accumulated)
P = monthly deposit
r = interest rate per period (monthly interest rate)
n = number of periods (number of monthly deposits)
Let's calculate the monthly interest rate (r):
r = 12% / 100% / 12 = 0.01
Now we can calculate the total amount accumulated (FV):
FV = 900 * ((1 + 0.01)^30 - 1) / 0.01
Using a calculator, compute (1 + 0.01)^30 - 1 = 0.4403, then divide 0.4403 by 0.01 to get a result of 44.03.
FV = 900 * 44.03 = $39,627
Now, to find the interest earned, we subtract the total amount of deposits made from the total amount accumulated:
Interest Earned = Total Amount Accumulated - Total Amount Deposited
Interest Earned = $39,627 - ($900 x 30)
Interest Earned = $39,627 - $27,000
Interest Earned = $12,627
Therefore, the interest earned after 2.5 years is $12,627.