Final answer:
To calculate the total amount of interest earned, use the formula A = P(1 + r/n)^(nt) - P, where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the provided values, the interest earned in 10 years is approximately $3,158.40.
Step-by-step explanation:
To calculate the total amount of interest earned, we can use the formula:
A = P(1 + r/n)nt - P
Where:
- A is the future value of the investment, which includes both the initial deposit and the interest earned
- P is the principal amount (the initial deposit)
- r is the annual interest rate (expressed as a decimal)
- n is the number of times interest is compounded per year
- t is the number of years
In this case, the principal (P) is $5,000, the annual interest rate (r) is 5%, the number of times interest is compounded per year (n) is 4 (quarterly compounding), and the number of years (t) is 10. Plugging these values into the formula:
A = 5000(1 + 0.05/4)4*10 - 5000
Simplifying the equation, we get:
A = 5000(1 + 0.0125)40 - 5000
Calculating this value, we find A ≈ $8158.40. So the interest earned in 10 years is:
Interest = A - P = 8158.40 - 5000 = $3158.40