What happens if a loan has an effective annual interest rate $i = 10$% is repaid with 10 yearly payments starting one year after the loan. The amount of the first payment is $500$ but each subsequent payment is $10$ larger than the previous payment.
Similar to the other question I asked in loan repayment- find the loan and interest paid.
I found the loan using $$\require{enclose} L = 500\left(1-(1/1.1)^{10}\right)/0.1 =3072.283 $$
I did a table to check what the outstanding balance will be at 10th payment but I get negative outstanding balance. Does that make sense?
The remaining debt after each payment is calculated by first applying the interest then deducting the amount paid. Therefore the remaining debt after each payment is as follows:
and so on, up to the zero residual debt after last payment:
$P(1+i)^{10}-500(1+i)^9-510(1+i)^8-...-580(1+i)-590=0$
This residual zero debt helps calculate the loan P:
$P=\frac{\sum_{k=0}^{9}{(500+10k)(1+i)^{9-k}}}{(1+i)^{10}}$
Using i=10%, I’ve got P=3301.19