A loan is usually paid back in a series of equal payments. Hence, the outstanding balance may be construed as half of the initial amount of the loans and the average interest paid is construed to be half the prescribed normal interest rate.
For example, Rs. 1000 were borrowed for a year at 6% and paid back in monthly installments, the average outstanding balance may be about Rs. 500 (meaning that the borrower over a year's time initially had the use of only Rs. 500 on the average) and the average interest paid would be about 3% of the initial amount or Rs. 30 in total. But if Rs. 60 were charged as interest on this same loan - present initial amount - the true interest rate would be nearly 12 percent as Rs. 60 is paid on average loan of only Rs. 500.
Thus, Average Interest = l/2((n+1)/n)
where 'i' is the interest rate and 'n', the number of years.
This formula is actually only a rough approximation of the capital recovery factor less the straight line depreciation rate. Taking an example, the average interest on a 6% rate for 10 years loan is approximated at 3.30 percent by using the average interest formula while the capital recovery factor (0.1359) less the straight line depreciation rate (0.100) sets the actual average interest rate. That is why, the use of average interest formula in the area of engineering economics is very rare.
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