You will be able to explain, with a worked example, why a flat rate understates the true yearly cost of borrowing.
A colleague tells you she is taking a S$10,000 personal loan to clear some bills and pay for her sister's wedding gift. The rate is 3% a year over five years, she says, which is less than her savings account earned at one point, so it is practically free. If that 3% is a flat rate, the loan costs her close to twice what she thinks, and she has no way of seeing it from the number she was given.
This lesson takes one loan, works through it month by month, and shows you where the hidden half of the cost comes from. All the figures are an example.
The offer is S$10,000 at 3% flat over five years, repaid monthly.
Flat interest is worked out once, on the full sum, for every year of the term. That is S$10,000 times 3% times 5 years, which is S$1,500. Add it to the loan and she repays S$11,500. Spread over 60 months, each instalment is S$11,500 divided by 60, about S$191.67.
Nothing in that calculation is false. The lender has told her the truth about the instalment and the total. The problem is the word "3%", which suggests she is paying 3% a year for the use of S$10,000. She is not, because she does not have the use of S$10,000 for five years.
Each S$191.67 instalment pays back part of the loan as well as interest. After the first month she owes less than S$10,000. After a year she owes roughly four-fifths of it. By the middle of the term she owes about half, and in the last few months she owes very little.
Averaged over the five years, she owes a little over S$5,300 at any one time. Yet she pays S$300 of interest every year, the same amount in year five as in year one, because the flat rate is charged on the original S$10,000 throughout. Paying S$300 a year to borrow an average of about S$5,300 is a rate of about 5.6%, not 3%.
The proper way to measure this is the effective interest rate from lesson 3.1, Advertised rate, APR and EIR are three different numbers. It asks: what yearly rate, charged only on the balance still owed, would make sixty payments of S$191.67 exactly repay S$10,000?
The answer is about 5.6% a year. You will calculate it yourself with a spreadsheet function in lesson 3.4, but you can see the logic already. On a reducing balance at 5.6%, the interest in the first month is about S$47, because she owes the full S$10,000. By the last month it is under a dollar. Across the first year the interest comes to about S$519, and across the fifth year about S$69. The flat rate loan charges S$300 in both years. The total is the same S$1,500 either way, but the reducing-balance version shows honestly that most of the cost falls early, when most of the money is still borrowed.
So a 3% flat rate on this loan is the same price as about 5.6% on a reducing balance. That is close to double the headline.
A flat rate loan always looks cheaper than it is, whatever the term, because the interest is charged on money already repaid. For terms of a few years at low flat rates, the EIR lands at a little under double the flat rate, and it does not move much as the term gets longer.
What does grow with the term is the money. At 3% flat, S$10,000 over five years costs S$1,500 in interest. Over seven years it costs S$2,100. The monthly instalment is lower on the longer loan, which makes it feel cheaper, yet the total paid is higher, and the misleading 3% now applies to seven years instead of five. This is why car loans and longer personal loans are the ones to check most carefully. They run for years, the sums are large, and the flat rate is the figure on the banner.
If you had to put this to your colleague in one sentence, it would be this: a flat rate charges you interest on the whole loan for the whole term, though you owe less every month, so the true yearly cost is close to twice the number quoted. She can still decide the loan is worth it. She will just be deciding on the real price.
The worked example used a five-year term. The quickest way to build your own feel for flat rates is to keep the same loan and rate and change only the term, then see which numbers move and which barely do.
Take the worked example, change the term to 3 years and then 7 years, and note how little the EIR moves while the total interest grows.
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