You will rebuild a money calculation from an advert, a quote or an assistant answer and see whether it holds.
The renovation contractor gave Joanne a brochure from a lender it works with. It offered S$10,000 at 3% a year over five years, with a monthly instalment of S$191.67. Next to it, in smaller type, was a line about an effective interest rate. Joanne had two numbers that didn't match and no idea which one to believe.
Every quote, projection and chat answer you're shown is the output of a calculation someone else did. This exercise takes one of them apart and rebuilds it, so you can see whether it holds and, if it doesn't, why.
Choose one money figure that came from somewhere else. Good candidates are a loan quote with an instalment, a savings or insurance projection showing what you'd have in some years, or an assistant's answer to a calculation question, such as the one you tried in lesson 5.1, Why the numbers in a paragraph can be wrong.
Pick something with a clear result you can compare against: a monthly payment, a total repaid, a value at a future date. Avoid figures that depend on unknown future returns, such as a projection at an assumed rate of growth, unless the document states the rate it used.
Joanne picked the loan brochure. Her figures are used below as the worked example.
Before you touch a spreadsheet, write down everything the calculation must have used. For a loan, that's the amount, the rate, the type of rate, the term, how often payments are made, and any fees. For a savings projection, it's the starting sum, the regular saving, the rate, how often interest is added, the term, and whether fees or charges are taken off.
Mark each input as stated in the document, assumed, or missing. Joanne's list: amount S$10,000, stated. Rate 3% a year, stated. Type of rate: missing, but the brochure didn't say "reducing balance" anywhere. Term five years, stated. Payments monthly, stated. Fees: the brochure mentioned a processing fee without a figure, so missing.
For anything missing, ask the provider in writing. Joanne emailed the lender to ask whether the 3% was a flat rate and what the processing fee would be. While she waited, she worked with what she had.
Set up a sheet with each input in its own labelled cell, as you did in lesson 5.2, Ask for the formula, then run it yourself. Then try to reproduce the figure you were given.
Joanne tried the reducing-balance formula first: =PMT(B2/12, B3*12, -B1), with 3% in B2. That gave S$179.69, not S$191.67. So the brochure wasn't using a reducing balance. She then tried a flat rate, using the method from How money works lesson 3.2, Why a flat rate loan costs nearly double what it looks like. Interest is S$10,000 times 3% times five years, which is S$1,500. The total repaid is S$11,500. Divided by 60 months, that's S$191.67. Match.
Now she knew what the 3% meant. The last step was to find its true yearly cost, using RATE as How money works lesson 3.4, Calculate the EIR of a flat rate offer with the RATE function, teaches: =RATE(60, -191.67, 10000)*12. The result is about 5.64% a year. That's the figure the small type was gesturing at, and it's the one to compare with other loans.
Before trusting it, she ran the estimate from lesson 5.3, Sanity-check results with a rough estimate. S$1,500 of interest over five years is S$300 a year. On average she owes about half the loan, S$5,000. S$300 on S$5,000 is 6%. The formula gave 5.64%, which is in the right range. Every figure here is an example, but the pattern holds for any flat rate quote.
Put your result next to the original and write down where they differ and why. The explanation should name the assumption that accounts for the gap, not just the size of it.
Joanne's note read: "The brochure's 3% is a flat rate, charged on the full S$10,000 for all five years. The instalment of S$191.67 is correct for that. The true cost on a reducing balance is about 5.6% a year, before the processing fee, which the lender hasn't told me yet. Any fee will push it higher."
If you rebuilt an assistant's answer and got a different figure, the explanation is often one you've seen in this module: a monthly figure treated as yearly, compounding at the wrong frequency, or deposits treated as a lump sum. Name the one that fits.
Sometimes you won't be able to explain the gap, because an input is still missing. That's a valid result. Write down which input you need and who can give it to you.
A sheet with labelled inputs, your rebuilt figure, the original figure beside it, your rough estimate, and a short written note on the difference. Keep it. The next time you see a quote like it, you'll only need to change the inputs.
Find your figure now. The best ones are those you were about to act on.
Rebuild one calculation in a spreadsheet, compare your result with the original, and write two sentences explaining any difference.
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