Final answer:
The question is about using the future value formula for compound interest to calculate how much a $24,000 deposit will grow to over 33 years at an APR of 6.1% with quarterly compounding.
Step-by-step explanation:
The subject of the question is Mathematics, specifically in the financial mathematics area, dealing with the calculation of the future value of an investment with compound interest. The question refers to a deposit of $24,000 at an Annual Percentage Rate (APR) of 6.1% with quarterly compounding over a period of 33 years. To find the future value of this deposit, you would need to use the future value formula for compound interest:
FV = P <1 + (r/n)>^(nt)
Where:
FV = Future value of the investment
P = Principal amount (initial deposit)
r = Annual interest rate (decimal form)
n = Number of times the interest is compounded per year
t = Number of years the money is invested or borrowed for
For the given problem, you would substitute the following values into the formula:
- P = $24,000
- r = 6.1% or 0.061
- n = 4 (since the interest is compounded quarterly)
- t = 33 years
You would then calculate the future value to determine the total amount of the investment after 33 years.