We all know that when we borrow money, we have to pay back the amount we borrowed plus an extra charge: the interest. Interest is the lender’s return on investment (a loan is actually considered an investment by lenders).
The interest charged on borrowing is normally expressed as an annual percentage rate, known as the APR; this is usually a higher figure than the actual interest charged however. Comparing the APR of loans is a quick and convenient way to compare two or more similar loans, the loan with the lowest APR being the better value.
The APR, however, does not represent the true cost of a loan. The timescale the loan is repaid over has the biggest influence on its cost: the longer the loan period, the more costly it becomes. This can give the illusion of a loan with a very reasonable sounding APR being good value when in reality it is extremely costly. Lenders pushing “low cost loans” rely heavily on this illusion.
Compound interest.
Borrowing £10,000 over one year at 5% (approximately 9.1% APR) would mean paying £500 in interest, as that is exactly 5% of the amount borrowed. What if £10,000 was borrowed over 2 years at 5%, how much interest would be charged? The answer is £1,025 (not £1,000).
The reason is down to compounding. Compound interest is where the interest charged grows exponentially with time. Effectively, it's a case of interest being charged on the interest already added.
The standard formula for compound interest is:
Borrowing £10,000 at 5% (or 0.05 as a number) for 5 years results in the following calculation: 10,000 * 1.055
The key to this formula is that the interest rate is raised to the power of the number of years that the money is borrowed over. This is where the real cost of the borrowing comes from: the interest accelerates as the loan length increases.
Using the example figures above, here's a table of how borrowing at 5% becomes extremely costly due to the compounding of interest:
Amount borrowed |
Interest rate |
Number of years |
Amount repayable |
Interest paid |
Interest as a percentage of borrowing |
£10,000 |
5% |
1 |
£10,500.00 |
£500.00 |
5.00% |
£10,000 |
5% |
2 |
£11,025.00 |
£1,025.00 |
10.25% |
£10,000 |
5% |
5 |
£12,762.82 |
£2,762.82 |
27.62% |
£10,000 |
5% |
10 |
£16,288.95 |
£6,288.95 |
62.89% |
£10,000 |
5% |
15 |
£20,789.28 |
£10,789.28 |
107.89% |
£10,000 |
5% |
20 |
£26,532.98 |
£16,532.98 |
165.32% |
As can be seen from the table, compounding accelerates the amount of interest
paid as a function of time. Borrowing over 20 years, for example, does not make
the interest 20 times larger than the one-year amount. The compounding of interest
increases it to 33 times the one-year amount.
Disguising this fact is where the advertising trickery comes in. Consolidation loans etc. are being advertised as a low cost option; an easy way to get out of debt. They do this by stressing the low APR. As can be seen though, it is possible to borrow at 5% yet pay back far more in interest than was actually borrowed in the first place. The APR may be low, but the interest as a percentage of borrowing, the true cost, increases rapidly the greater the duration of the loan.
It should be clear why loan companies are encouraging people to take out large loans over an extended period. They are not really interested in helping people to lower their monthly payments; they understand the earning power of compound interest.
More info:
UK Skeptics' loan calculator and analyser.
