Final answer:
To determine the interest rate for a $6000 deposit that grows to $6536 after 9 years with annual compounding, the compound interest formula is used. The interest rate, when solved using the formula, is found to be approximately 0.95% per year.
Step-by-step explanation:
The student is interested in finding the interest rate for a $6000 deposit that grows to $6536 after being compounded annually for 9 years. This question involves the concept of compound interest which can be calculated using the compound interest formula:
A = P(1 + r/n)nt
In this formula, A is the amount of money accumulated after n years, including interest. P is the principal amount (initial deposit), r is the annual interest rate (in decimal), n is the number of times that interest is compounded per year, and t is the time in years.
Since the interest is compounded annually, n = 1. The problem given provides A = $6536, P = $6000, and t = 9 years. We need to solve for r, which requires rearranging the formula:
r = (A/P)1/nt - 1
Substituting the known values:
r = ($6536/$6000)1/(1\times9) - 1
r = 1.0893331/9 - 1
r ≈ 0.009547 or about 0.95%
So, the annual interest rate that would allow a $6000 deposit to grow to $6536 in 9 years, when compounded annually, is approximately 0.95%.