Reducing balance and flat rate loans can both be used to borrow funds and each have advantages and disadvantages.

## Which is Better?

Financially, reducing balance loans are more beneficial to the borrow than flat rate loans because:

• Reducing balance loans are calculated on the amount owing each period which decreases continuously during the life of the loan
• Flat rate loans are calculated on the amount borrowed

### Example 1

A $24,000 loan is repaid over five years where interest is compounded quarterly at 8.7% p.a. . Instalments of$1,492.67 are repaid quarterly.

a) What is the total amount of interest paid?

Calculate the amount of interest periods.

$n=5\times 4$
$n=20$

To find the amount of interest, multiply the instalment value by the number of periods and subtract the principal.

Interest $=1,492.67\times 20-24,000$
Interest $=5,853.4$

The total interest paid is $5,853.40. b) What amount could be borrowed using a flat rate loan (where all other variables are unchanged) to the nearest dollar? We will use the simple interest formula- write the values of each of these terms. $I=5,853.4$ $r=8.7$ $T=5$ Transpose the formula to find P. $I=\dfrac{PrT}{100}$ $P=\dfrac {100\times I}{r\times T}$ $P=\dfrac {100\times 5,853.4}{8.7\times 5}$ $P=13,456.092$ Where all variables remain constant, a flat rate loan of$13,456 could be borrowed.

c) What is the difference in the amount borrowed between the two loans (to the nearest dollar)?

Find the difference in the loans by subtracting the smaller amount from the larger amount.

Difference $=24000-13,456$
Difference $=10,543.908$

There is a difference of $10,544. Under the same conditions a$24,000 reducing balance loan is equivalent to a \$13,456 flat rate loan.