Final answer:
To find the closest value to the end value of an investment with compound interest, we apply the formula for compound interest using the principal amount of $7,500, annual interest rate of 12.36%, compounded semiannually, over a period of 2.5 years.
Step-by-step explanation:
To find the closest value to the end value of investing $7,500 for 2 1/2 years at an effective annual interest rate of 12.36%, compounded semiannually, we can use the formula for compound interest:
A = P(1 + r/n)nt
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
Using the given values:
- P = $7,500
- r = 0.1236
- n = 2 (since interest is compounded semiannually)
- t = 2.5 years
Plugging these into the formula, we get:
A = 7500(1 + 0.1236/2)2*2.5
Calculating this gives us the total accumulated amount. We can then compare the calculated amount to the given options to find the closest value.
Compound interest as seen in these calculations can result in significant growth of an investment over time, particularly with higher rates and longer time periods, as shown in the referenced information where even small amounts can grow substantially.