Hi, I would appreciate any help with the following exercise in financial maths. I'm a lawyer and I'm quite lost with the approximation technique to find the interest.
You borrow $ 1000 from a loan shark and are offered a choice of two possible loan repayment schemes:
- 20 monthly repayments of $ 100, with the first repayment being one month after you borrow the $ 1000.
- 10 monthly repayments of $80, with the first repayment being one month after you borrow the $ 1000 followed by a singl repayment of $800, 11 months after you borrow the $ 1000.
a) Determine* the effective interest rate J12 that you are being charged in the first option.
b) Determine* the effective interest rate J12 that you are being charged in the second option, and thus identify which of the two options is preferable.
*Within an accuracy of +/- 1.2% which implies that you will need to find i to an accuracy of +/- 0.1%.
Your help is much appreciated.
Jake, because this is an assignment I have to show some procedures in my answers. What they want us to do is to use the iterative approach (replacing different values for i in the present value annuity formula:
I already did it with question 1 (20 payments of 100 to pay off 1000 loan).
But I don't know where to start with question 2 (10 payments of 80 and 800 at the end on the eleventh period). I don't know how to manage the $800.
If you have an idea I'd appreciate your help or anyone's else.
You can add present values. So you can use the formula to calculate the PV of the 10 payments as a function of i. Then you can add the PV of 800 (which is 800/(1+i)^11) to get the total PV. Then you can iterate on i using the total PV the same as for question 1.