Question

An individual wishes to borrow $10,000 for a year and is offered the following alternatives:

a. A 10 percent loan discounted in abvances

b. An 11 percent straight loan (interest paid at maturity)

Which loan is more expensive?

Step 1

Calculating the effective interest rate on borrowing option 10% loan discounted in advances. We have,

In the advance discounting option, we shall require higher amount to borrow. Therefore, the amount needed to borrow in this option are as follow:

Total amount to borrow = Proceeds to be used / (1 – rate of interest)

Total amount to borrow = $ 10,000 / (1 – 0.10)

Total amount to borrow = $ 11,111.11

The effective interest rate on the borrowing = (Total amount to borrow / Proceeds to be used) - 1

The effective interest rate on the borrowing = ($ 11,111.11 / $10,000) - 1

The effective interest rate on the borrowing = 1.1111 – 1 = 0.1111*100

The effective interest rate on the borrowing = 11.11 %

Step 2

Calculating the effective interest rate on borrowing option 11% straight loan. We have,

Total amount to borrow = Proceeds to be used (1 + interest rate)

Total amount to borrow = $ 10,000 (1.11)

Total amount to borrow = $ 11,100

The effective interest rate on the borrowing = (Total a...

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