Final answer:
To determine the total amount and compound interest on $5,000 at 8% over 20 years, the formula for compound interest is applied with quarterly compounding. The resulting total is obtained from the formula A = P(1 + r/n)^(nt), and the interest earned is the difference between the total amount and the principal.
Step-by-step explanation:
The total amount and the amount of interest earned on $5,000 at 8% for 20 years, compounded quarterly, can be calculated using the compound interest formula: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time in years.
For quarterly compounding, the rate is divided by 4 and the years are multiplied by 4. The formula becomes A = $5,000(1 + 0.08/4)^(4×20). When calculated, the total amount A comes out to $5,000(1 + 0.02)^(80), which after using a calculator, gives us a value for A. To find the amount of interest earned, subtract the principal (P) from the total amount (A).
From Box 1.2: Interest Example, we know that compound interest can significantly increase earnings over time, especially with larger sums and longer time periods. This effect is more pronounced in compound interest than with simple interest, as demonstrated by the $0.76 difference after three years on a $100 principal in Step 8.