When a loan officer speaks to people about a loan for a certain principal, P, at a certain monthly rate, r, they always have to balance two quantities, the monthly payment, m, with the number of payments, n, it takes to pay off the loan. These two vary inversely. All of these quantities can be related by the formula:

The Required formulae is  .

Given,

For a certain loan amount, principal is p, rate of interest is monthly denoted by r, no of payment is n and the monthly payment is m.

The formulae for relating all the quantities is given by,

Here p is principal, r is the rate of interest and is the number of payment .

Hence the Required formulae is  .

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Step-by-step explanation:

When you take a loan, the amount collected is referred to as the Principal(P).

The loan is given at a certain rate(r) in this case a Monthly Rate for a period of n months. The Monthly payment is denoted using M.

All these variables are related by the function:

Note that if the rate is given as an Annual rate, we divide by 12 to get the monthly rate required.