Final answer:
To calculate the future value of a $7,500 investment at a 12.5% annual interest rate over 30 years, use the compound interest formula FV = P(1 + r)^n. The future value (FV) is then calculated as $7,500 * (1.125)^30.
Step-by-step explanation:
The subject in question involves calculating the future value of an investment with compound interest. To find the value of a $7,500 investment increasing at a rate of 12.5% per year for 30 years, one would use the formula for compound interest:
FV = P(1 + r)^n
Where:
- FV is the future value of the investment.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of years the money is invested.
Plugging in the values, we get:
FV = $7,500(1 + 0.125)^30
Now, let's do the math:
Calculate the multiplier: (1 + 0.125) = 1.125
Raise 1.125 to the power of 30: 1.125^30
Multiply the principal amount $7,500 by the multiplier:
Final calculation: $7,500 * (1.125)^30
To find the exact future value, you'd use a calculator for the expression above to get the ending balance of the investment after 30 years.