The banks offers a rate of 8 1/4 percent with a 20percentcompensating balance requirement, or as an alternative, 9 3/4 percent with additional fees of 5,500 to cover services the bank is providing. In either case the rate on the loan is floating ( changes as the prime interest rate changes) and the loan would be for one year.
A. Which loan carries the lower effective rate?Consider fees to be the equivalent of other interest.
B. If the loan with a 20 percent compensating balance requirement were to be paid off in 12 months, what would the effective rate be? (principal equals amount borrowed minus the compensating balance).
To determine the effective rate for each loan option, we need to consider both the stated interest rate and any additional fees or requirements. Let's calculate the effective rate for each loan:
A. To find the effective rate, we need to account for the compensating balance requirement and fees.
For the first loan option with an 8 1/4 percent rate and a 20 percent compensating balance requirement, we consider the fees to be equivalent to interest.
To calculate the effective rate, we subtract the compensating balance percentage from 100 percent. In this case, 100% - 20% = 80%.
Then, we divide the stated interest rate by the effective percentage.
Effective rate = Stated interest rate / Effective percentage
Effective rate = 8.25% / 80% = 10.3125%
Therefore, the first loan option has an effective rate of 10.3125%.
B. For the second loan option with a 9 3/4 percent rate and additional fees of $5,500 to cover services provided by the bank, we need to include the fees in the calculation.
First, we add the fees to the loan amount to get the total amount borrowed.
Total amount borrowed = Loan amount + Fees
Assuming the loan amount is x,
x + $5,500 = Total amount borrowed
Then, we calculate the effective rate by dividing the total amount borrowed by the loan amount and converting it to a percentage.
Effective rate = (Total amount borrowed / Loan amount - 1) × 100
Effective rate = ((x + $5,500) / x - 1) × 100
As the loan is to be paid off in 12 months, the effective rate will be calculated based on the total amount repaid (principal plus interest) over the loan duration.
Remember that the principal equals the amount borrowed minus the compensating balance requirement. So, for the second loan option, the principal would be x - (20% * x) = 0.8x.
To determine the effective rate, we need the loan amount x. Unfortunately, it is not provided in the question. Once we have the loan amount, we can calculate the effective rate using the formula mentioned above.