Let Ln be the unpaid balance on a loan with an interest rate, r, per term. A payment of P is made at the end of each year.
a) Lo, is original amount borrowed. Construct a loan payment model for the unpaid balance at the end of each year.
I was thinking Ln= (Lo-P)r. I'm not entirely sure though.
b) Find the balance after 3 years when payments of 500 are made quarterly on an original loan of $9600 with an interest rate of 10.5% each quarter.
Again I'm not sure what to do. I don't know if my model is correct. Also how does quarterly change this (I know it does but not sure how).
c) Find the balance after 5 years when a payment of 400 is made monthly on an original loan of $20,000 with annual interest of 8%.
In each period, you charge interest on the balance and deduct any payments made. So if the balance at the start of the period is $L$ the balance at the end of the period before the payment is $L(1+r)$ and the balance after the payment is $L(1+r)-P$. That is the starting balance for the next period.