Question

If an account starts with $5,000 and earns 1% interest per year, compounded quarterly, find its future value after 11 years. (Enter an answer correct to the nearest cent.)

(A) $5,000.25
(B) $5,556.06
(C) $5,513.25
(D) $5,228.33

Answer 1

To find the future value of the account, you can use the formula A = P(1 + r/n)^(nt), where A is the future value, P is the principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years. Substituting the given values into the formula, the future value is approximately $5,556.06.

Step-by-step explanation:

To find the future value of an account with compound interest, we can use the formula:

A = P(1 + r/n)^(nt)

Where:
A = future value
P = principal (starting amount)
r = interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years

Given that the principal is $5,000, the interest rate is 1% (which is 0.01 as a decimal), the interest is compounded quarterly (n = 4), and the time period is 11 years, we can substitute these values into the formula:

A = 5000(1 + 0.01/4)^(4*11)

Calculating this expression gives us a future value of approximately $5,556.06. Therefore, the correct answer is (B) $5,556.06.