A company plans to borrow $2 million for a year. The stated interest rate is 12 percent. Compute the effective interest rate under each of these assumptions. Each part stands alone. a. The interest is discounted. b. There is a 20 percent compensating balance requirement. c. It is a 12-month install

Question

A company plans to borrow [latex]\$ 2[/latex] million for a year. The stated interest rate is 12 percent. Compute the effective interest rate under each of these assumptions. Each part stands alone.

a. The interest is discounted.

b. There is a 20 percent compensating balance requirement.

c. It is a 12-month installment loan.

d. Assume the interest is only [latex]\$ 45,000[/latex] and the loan is for 90 days.

Accepted Answer

[latex]\begin{aligned} ext { a. Effective rate on discounted loan } &=\frac{ ext { Interest }}{ ext { Principal }- ext { Interest }} \ & imes \frac{ ext { Days in the year }(360)}{ ext { Days loan is outstanding }} \ &=\frac{\$ 240,000}{\$ 2,000,000-240,000} imes \frac{360}{360} \ &=\frac{\$ 240,000}{1,760,000} imes 1=13.64 \% \end{aligned}[/latex]

b. Effective rate with compensating balances

[latex]\begin{aligned} =\frac{ ext { Interest }}{ ext { Principal }- ext { Compensating balance in dollars }} imes \frac{ ext { Days in the year }(360)}{ ext { Days loan is outstanding }}\end{aligned}[/latex]

Compensating balance [latex]=20 \% imes \$ 2,000,000=\$ 400,000[/latex]

Effective rate [latex]=\frac{\$ 240,000}{1,600,000} imes 1=15 \%[/latex]

c. Effective rate on installment loan

[latex] \begin{array}{l} =\frac{2 imes ext { Annual number of payments } imes ext { Interest }}{( ext { Total number of payments }+1) imes ext { Principal }} \ =\frac{2 imes 12 imes \$ 240,000}{(12+1) imes \$ 2,000,000} imes \frac{\$ 576,000}{2,600,000}=22.15 \% \end{array} [/latex]

[latex]\begin{aligned} ext { d. Effective rate } &=\frac{ ext { Interest }}{ ext { Principal }} imes \frac{ ext { Days in the year (360) }}{ ext { Days loan is outstanding }} \ &=\frac{\$ 45,000}{\$ 2,000,000} imes \frac{360}{90}=2.25 \% imes 4=9 \% \end{aligned}[/latex]

Question 8.2: A company plans to borrow $2 million for a year. The stated ...

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