The treasurer of Brandon Blue Sox is seeking a $32,000 loan for 180 days from the Brandon Credit Union. The stated interest rate is 14 percent and there is a 20 percent compensating balance requiremen
t.
To calculate the compensating balance, we first need to find out how much the treasurer needs to borrow. The compensating balance is based on the loan amount, not including the interest.
Loan amount = $32,000
Now, we can calculate the required compensating balance:
Compensating balance = 20% * Loan amount = 20% * $32,000 = $6,400
The treasurer will need to keep a compensating balance of $6,400 in their account with the credit union.
To calculate the interest on the loan, we can use the following formula:
Interest = Loan amount * Interest rate * Time
Loan amount = $32,000
Interest rate = 14% (0.14 as a decimal)
Time = 180 days / 365 (since most interest rates are quoted on an annual basis)
Interest = $32,000 * 0.14 * (180/365) = $785.75
Therefore, the treasurer will need to pay $785.75 in interest on the loan.
In summary, the treasurer of Brandon Blue Sox needs to get a $32,000 loan from the Brandon Credit Union for 180 days. They will be required to maintain a compensating balance of $6,400 and will need to pay $785.75 in interest on the loan.
To calculate the loan amount and the total interest paid, follow these steps:
Step 1: Calculate the compensating balance requirement:
- Multiply the loan amount by the compensating balance percentage (20% or 0.2)
- Compensating balance = Loan amount x Compensating balance percentage
Step 2: Calculate the effective loan amount:
- Effective loan amount = Loan amount - Compensating balance
Step 3: Calculate the interest owed:
- Interest = Effective loan amount x Interest rate x Time
- Time is given as 180 days, so we divide it by 365 to get it in years.
Step 4: Calculate the total amount to be repaid:
- Total repayment = Loan amount + Interest
Now let's calculate the loan amount, the compensating balance, the effective loan amount, the interest, and the total amount to be repaid.
Given:
Loan Amount = $32,000
Stated Interest Rate = 14%
Compensating Balance Requirement = 20%
Time (in years) = 180 days / 365 days/year
Step 1: Calculate the compensating balance:
Compensating balance = $32,000 x 0.2 = $6,400
Step 2: Calculate the effective loan amount:
Effective loan amount = $32,000 - $6,400 = $25,600
Step 3: Calculate the interest:
Interest = $25,600 x 0.14 x (180/365) = $659.12
Step 4: Calculate the total amount to be repaid:
Total repayment = $32,000 + $659.12 = $32,659.12
Therefore, the treasurer should expect to repay a total amount of $32,659.12, including both the loan amount and the interest.