The recursive formula below is used to construct a loan schedule: 

L(t) = (1+i)L(t-1) - X(t) 

where L(t) = Loan outstanding at end of period t X(t) = repayment at end of period t i = effective interest rate per unit of time t. 

i. Explain in words what this formula is saying. 

ii. Generalise the formula to include a fee of $8 per unit of time t paid in addition to the repayment X(t). 

iii. Suppose the interest was calculated as continuously compounding with a force of interest d. Generalise the formula in Parti and define any additional terms to include this case.