Final answer:
To find out how long $5600 must be deposited at an annual rate of 7% to grow to $11,016.05, you use the compound interest formula. Calculating with the given figures yields approximately 10 years, making the correct answer option E) 10 years.
Step-by-step explanation:
To determine how long $5600 must be in a bank at 7% compounded annually to become $11,016.05, we can use the formula for compound interest, A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
In this case:
- A = $11,016.05
- P = $5600
- r = 7% or 0.07
- n = 1 (compounded annually)
We want to find t, so we rearrange the formula:
t = log(A/P) / (n × log(1 + r/n))
Substituting the values in:
t = log(11016.05/5600) / (1 × log(1 + 0.07))
After calculating, we find that t is approximately 10 years, which matches option E. Therefore, $5600 needs to be invested for approximately 10 years at an annual compound rate of 7% to grow to $11,016.05.
E) 10 years rounded to the nearest year.