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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%.

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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.

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    Thank you. Why is it L times (1+r) and not just L times r? appreciate the help – 2017-02-15
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    $Lr$ is the interest. It is added to the balance of the loan, which is $L$ If you borrow $1000$ at $10\%$ for one period, at the end you owe $1100$, not $100$. – 2017-02-15