Final answer:
To calculate the amount of money in the account after 10 years with quarterly compounding, we use the formula A = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, t is the number of years, and n is the number of times the interest is compounded per year. Plugging in the given values, the amount in the account after 10 years is approximately $24,654.28.
Step-by-step explanation:
To calculate the amount of money in the account after 10 years with quarterly compounding, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money in the account after t years
P = the principal amount invested ($15,000 in this case)
r = annual interest rate (5% in this case)
t = number of years (10 in this case)
n = number of times the interest is compounded per year (4 for quarterly compounding)
Plugging in the given values, we get:
A = 15000(1 + 0.05/4)^(4*10)
A = 15000(1.0125)^(40)
A ≈ 15000(1.6436184)
A ≈ $24,654.28