Finance Interview Questions: Riddles Solved Step by Step
Finance interviews mainly test successive percentages, the time value of money and how to read rates. Here are 4 classic riddles, each with its solution worked out step by step.
Portfolio Down 50% Then Up 50%: Why You Don't Break Even
Finance job interview question
A portfolio is worth €100. It loses 50% of its value, then gains 50% on the value it then has. How much is it worth at the end? What percentage gain would be needed to get back to €100 from €50?
Need a hint?
Calculate each change on the value at that moment, not on the starting value.
Show the answer and the solution
Answer: €75 after both changes, a loss of 25%; to get from €50 back to €100, a gain of 100% is needed.
The reasoning
After the 50% loss, the portfolio goes from €100 to €50. The 50% gain applies to €50, not to €100: it adds €25, so the portfolio is worth €75. The total loss is therefore 25% (from €100 to €75). To get from €50 back to €100, the sum must double, so a gain of 100% is needed. A 50% rise does not offset a 50% fall, because the base of the calculation changes. Successive percentages do not simply add up.
Present Value of €100 in One Year at a 5% Discount Rate
Banking job interview question
An investment will pay you €100 in one year. The discount rate is 5% per year. What is the present value of this payment, that is, what is it worth today? Round to the nearest cent.
Need a hint?
Ask yourself what amount, invested today at 5% for one year, would give €100, and think of the reverse of compounding.
Show the answer and the solution
Answer: About €95.24: €100 divided by 1.05, since €95.24 invested at 5% becomes €100 in one year.
The reasoning
An amount of €100 received in one year is worth less than €100 today, because the money could be invested in the meantime and earn interest. To find the present value, we look for the amount that, compounded at 5% for one year, gives €100. If V is this amount, V × 1.05 = 100, so V = 100 / 1.05, or about €95.24. Check: 95.24 × 1.05 = 100.002, or €100 to the nearest cent. This calculation illustrates the time value of money: €95.24 today is worth €100 in one year at 5%.
Monthly 1% Interest: Effective Annual Rate Is Not 12%
Banking question: converting a monthly rate to an effective annual rate
An investment earns 1% per month, with compound interest every month: each month's interest is added to the capital, which then earns the following interest. What is its effective annual rate, that is, the real increase in capital over one year, and is it really 12%?
Need a hint?
Instead of adding the rates month after month, multiply the capital by the factor for one month and repeat this multiplication twelve times.
Show the answer and the solution
Answer: No: the effective annual rate is about 12.68%, because 1.01 to the power 12 is about 1.1268.
The reasoning
With compound interest, the capital is multiplied by 1.01 each month, since the interest earned is reinvested. After twelve months, it has therefore been multiplied by 1.01 to the power 12, which is about 1.126825. The effective increase over the year is thus about 12.68%. The 12% rate corresponds only to simple interest, where interest earned does not itself earn interest. Compound interest therefore adds about 0.68 percentage points to the nominal 12% rate. In banking, you should always convert a monthly rate into an effective annual rate before comparing two investments.
Markup vs Margin on the Same Item: Why the Rates Differ
Classic corporate finance trap on margin and markup rates
A retailer buys an item for €80 and resells it for €100. What is the retailer's margin rate, calculated on the selling price, and its markup rate, calculated on the purchase price?
Need a hint?
Ask yourself each time which price is the base for the percentage calculation, then calculate the gain before dividing it.
Show the answer and the solution
Answer: Margin rate of 20% (€20 on €100) and markup rate of 25% (€20 on €80): they are not equal.
The reasoning
The gross margin on the item is the difference between the selling price and the purchase price: €100 minus €80 = €20. The margin rate is calculated on the selling price: 20 / 100 = 0.20, or 20%. The markup rate is calculated on the purchase price: 20 / 80 = 0.25, or 25%. Both percentages measure the same €20 gain, but their bases differ, which explains the gap. So always state the base of a calculation before comparing two percentages.
Frequently asked questions
What kinds of finance riddles are on this page?
The riddles on this page cover three topics: successive percentages, the present value of a sum, and rates, including the margin rate and the markup rate. A common trap is adding percentages that apply to different bases.
Do you need to memorize formulas for these finance riddles?
No, it is enough to know how to set up a multiplication or a division: discounting means dividing by 1 plus the rate, and an effective annual rate is found by raising 1 plus the monthly rate to the power of the number of periods. Remembering this reasoning is more useful than a memorized formula.
How should you prepare for these finance riddles?
Redo each computation step by step, without a device when possible, then check the result against an order of magnitude. Start with successive percentages and discounting, then move on to margin and markup rates, which differ by their base of computation.
What next?
Reasoning improves like memory: by practising often. Next, test yourself on our general knowledge quizzes.