Question

Your company plans to borrow $13 million for 12 months, and your banker gives you a stated rate of 24 per cent interest. You would like to know the effective rate of interest for the following types of loans. (Each of the following parts stands alone.)

c. An instalment loan (12 payments).

Short answer

The effective interest rate is 44.3%.

Step-by-step solution

Information provided in the question

Loan amount = $13,000,000

Loan term = 1 year

Interest rate = 24%

Number of payments = 12

Calculation of interest payable

The interest payable is $3,120,000.

$\begin{array}{rcl}\mathrm{Interest}\mathrm{payable}& =& \mathrm{Interest}\times \mathrm{Principal}\\ & =& 24\%\times \$13,000,000\\ & =& \$3,120,000\end{array}$

Calculation of effective interest rate on the instalment loan

The effective interest rate on an instalment loan is 44.3%.

$\begin{array}{rcl}\mathrm{Effective}\mathrm{rate}& =& \frac{2\times \mathrm{Annual}\mathrm{number}\mathrm{of}\mathrm{payments}\times \mathrm{Interest}}{\left(\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{payment}+1\right)\times \mathrm{Principal}}\\ & =& \frac{2\times 12\times \$3,120,000}{\left(12+1\right)\times \$13,000,000}\\ & =& \frac{\$74,880,000}{\$169,000,000}\\ & =& 44.3\%\end{array}$