Final answer:
Mark Welsch will have approximately $11,790.85 in his account at the end of 4 years, after depositing $8,000 with an interest rate of 8% compounded quarterly.
Step-by-step explanation:
To calculate the future value of Mark Welsch's deposit, we need to apply the formula for compound interest. The general formula is A = P(1 + r/n)nt, where:
- P is the principal amount (the initial amount of money)
- r is the annual interest rate (in decimal form)
- n is the number of times the interest is compounded per year
- t is the time the money is invested for, in years
In this scenario:
- P = $8,000
- r = 8% or 0.08 in decimal
- n = 4 (since the interest is compounded quarterly)
- t = 4 years
Substituting these values into the compound interest formula:
A = 8000(1 + 0.08/4)4*4
Let's do the math:
- Divide the annual interest rate by the number of compounding periods: 0.08/4 = 0.02.
- Add 1 to the result of step 1: 1 + 0.02 = 1.02.
- Raise the result of step 2 to the power of the total number of compounding periods: 1.0216 (since 4 years times 4 quarters per year equals 16 quarters).
- Multiply the principal amount by the result of step 3: $8000 * 1.0216.
- The final calculation gives us the future value of the investment.
Upon performing the calculations, we find that A is approximately $11,790.85.
This is the amount of money Mark will have in his account at the end of 4 years, including the principal and the compound interest earned over time.