Final answer:
The compounded annually interest rate charged on the loan is found using the compound interest formula. By plugging the given values into the formula and solving for the interest rate, we find that the annual interest rate is 3.6%, which matches option A.
Step-by-step explanation:
To find out the compounded annually interest rate charged on a $2500 loan that amounted to $3500 after 9.45 years when paid back, we can use the compound interest formula:
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.
Since the interest is compounded annually, n is 1. We know that A is $3500, P is $2500, and t is 9.45 years. Plugging these values into the formula, we get:
3500 = 2500(1 + r)^9.45
Divide both sides by 2500 to isolate the term with r:
1.4 = (1 + r)^9.45
Next, we take the 9.45th root of both sides to solve for (1 + r):
1.4^(1/9.45) = 1 + r
1.4^(1/9.45) - 1 = r
Now we perform the calculation:
r ≈ 0.036 or 3.6%
The annual interest rate charged by the bank is 3.6%, which corresponds to option A.