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.
a.$31,619.46
b.$31,306.40
c.$4,619.47
d.$4,306.40
(I can not figure this out, so please if you could walk me through it. )
To find the interest earned after 2.5 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (including interest)
P = Principal amount (initial deposit)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
In this case, Carly deposits $900 at the end of every month for 2.5 years, so the principal amount is $900 * 12 * 2.5 = $27,000.
The annual interest rate is 12%, which in decimal form is 0.12.
The interest is compounded monthly, so n = 12.
The time period is 2.5 years, so t = 2.5.
Plugging in these values into the formula, we get:
A = $27,000(1 + 0.12/12)^(12 * 2.5)
Now, we can calculate A to find the final amount:
A = $27,000(1 + 0.01)^(30)
A = $27,000(1.01)^(30)
Using a calculator, we get:
A ≈ $31,619.46
Therefore, the interest earned after 2.5 years is approximately $31,619.46.
Hence, the correct answer is (a) $31,619.46.