Further Maths Textbook

Reducing Balance Loans

Study Notes

When you buy a house most case you borrow from a bank. The bank requires interest from you, but at the same time you give some money back to the bank. At first balance is quite high however later balance reduces quickly. Here we discuss this theory mathematically.

If you borrow $P at annually compounded interest of r%, and make repayment $Q every month after one year of the loan

The balance A after n years is given A =  

Let 1–r/100 = R then  A = →

If interest is compounded monthly r →  r/12 and n → 12n

If interest is compounded quarterly r → r/4 and n → 4n

This formula is called annuities formula

 

Summary of the formula is as follows

PRn represents increasing Principal by interest and Rn  is the term to increase P.

The latter part is the sum of yearly repayments and their interest added each year.

In this formula repayment is 1/12 of yearly formula and at the same time interest is also 1/12 of the yearly formula. Therefore we just replace r with r/12 and index of R (how many time index is given) becomes 12 times (every months receiving interest but the interest is 1/12 of yearly one).

The formula in right hand side is convenient/easier if topic time is not years but months (like 15 months).

Quarterly formula can be understood by the same way as monthly formula.

Interest per annum becomes ¼ but paid 4 times a year.

â’» Understanding formula

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