Question

If ​$1285.00 accumulates to ​$1505.37 in three ​years, three months compounded quarterly, what is the effective annual rate of​ interest? Question content area bottom Part 1 The effective annual rate of interest is enter your response here​%. ​(Round the final answer to four decimal places as needed. Round all intermediate values to six decimal places as​ needed.)If ​$1285.00 accumulates to ​$1505.37 in three ​years, three months compounded quarterly, what is the effective annual rate of​ interest? Question content area bottom Part 1 The effective annual rate of interest is enter your response here​%. ​(Round the final answer to four decimal places as needed. Round all intermediate values to six decimal places as​ needed.)

Answer 1

The effective annual rate of interest is 7.97%.

Step-by-step explanation:

To find the effective annual rate of interest, we can use the formula A = P(1+r/n)^(nt), where A is the future amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, we have:

A = $1505.37

P = $1285.00

n = 4 (compounded quarterly)

t = 3.25 years (3 years and 3 months)

Substituting these values into the formula, we can solve for r:

$1505.37 = $1285.00(1+r/4)^(4*3.25)

Simplifying the equation, we have:

1.169223 = (1+r/4)^13

Taking the 13th root of both sides, we get:

1+r/4 = 1.01992

Solving for r, we subtract 1 from both sides and multiply by 4:

r = 0.0797, or 7.97%