Final answer:
Using the compound interest formula, and after calculation, it was found that $15,000 would earn approximately $6491.46 in 4 years with a 9.5% interest rate compounded quarterly. however, this answer does not match any of the provided options indicating there might be an error in the provided information.
Step-by-step explanation:
To find how much interest $15,000 earns in 4 years in a certificate of deposit (CD) paying 9.5% interest compounded quarterly, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
where:
- A = the amount of money accumulated after n years, including interest.
- P = the principal amount (the initial amount of money).
- r = the annual interest rate (decimal).
- n = the number of times the interest is compounded per year.
- t = the time the money is invested for, in years.
For this question:
- P = $15,000
- r = 9.5% or 0.095
- n = 4 (since the interest is compounded quarterly)
- t = 4 years
Plugging the values into the formula, we get:
A = 15000 (1 + 0.095/4)^(4*4)
Now, calculate the amount A:
A = 15000 (1 + 0.02375)^(16)
A = 15000 (1.02375)^(16)
A ≈ 15000 * 1.432764
A ≈ 21491.46
To find the interest earned, subtract the principal from the total amount:
Interest = A - P
Interest = 21491.46 - 15000
Interest ≈ $6491.46
However, none of the options given match the correct calculation. There might have been an error in the provided options or in the interest rate given.