Hello I haven't seen a particular question on this but I have been trying to prepare a loan schedule for payments that are made at the start of each year. I solved for the annual repayment using an equation of value with adue factors but I couldn't get the loan schedule to match up (as in, I couldn't get the loan outstanding at the end of the final year to be 0). I've tried using the discount factor d to obtain the interest element and various different ways to try and deduct the interest at the start of each year but nothing quite worked. No worries if this isn't examinable, but it's bugging me that I can't figure it out! If you could give me some tips on the formulas we'd use to prepare a loan schedule for payments made in advance please then I'd be really grateful! Thanks!
If the repayments are in advance then the final repayment will be at the start of the final year and not the end. And so try working out the loan outstanding at time n-1 instead of n. You'll still need an n-year annuity due, or knock the first payment off the loan amount at time 0 and work with an annuity in arrear for n-1 years. Hope that helps.
Hi Darrell Thank you so much for this. I have managed to set up a loan schedule and get the loan outstanding at time n-1 to be 0 by effectively assuming 100% of each repayment is capital, deducted from the loan outstanding at the start of the year, and then using i to work out the interest accrued over the year. I guess then effectively this can be thought of as the initial repayment having an interest element of 0 and being 100% capital, and then the second payment equal to the interest accrued over year 1 (= (initial loan - repayment at time 0) * i) and then plus a capital element ( = loan outstanding immediately after 1st repayment - loan outstanding immediately after 2nd repayment). Is this the correct way of thinking about it? Just thinking if we were ever asked for the interest/capital components that's all. Thank you ever so much! Lauren
Yep that makes sense. Hopefully all hypothetical - it would be a very unusual exam questions . I'd move on!
