R02 Compounding, discounting and present value: free practice questions

1. Question 1 of 5

   Why is £10,000 received today worth more than £10,000 received in three years' time?

   Option A: Inflation always increases the value of money over timeOption B: Money received now can be invested to earn interestOption C: Money received later is always taxed more heavilyOption D: Future sums can't be invested at all

   Show answer

   The answer is B: Money received now can be invested to earn interest

   This is the basic idea of the time value of money: a sum now can be invested and earn interest, so it's worth more than the same sum later.

   Why the other options are wrong

   A

   Inflation reduces the value of money, and isn't the core reason here.

   C

   Tax treatment isn't what the time value of money describes.

   D

   Future sums can be invested once they arrive, but they miss the earlier growth.

2. Question 2 of 5

   £10,000 is invested at 4% a year for two years, then the whole amount is reinvested at 6% a year for a further three years. What is it worth at the end?

   Option A: £12,166.53Option B: £12,882.03Option C: £12,638.97Option D: £13,382.26

   Show answer

   The answer is B: £12,882.03

   FV = £10,000 × 1.04² × 1.06³ = £10,000 × 1.0816 × 1.191016 = £12,882.03. Each bracket is calculated first.

   Why the other options are wrong

   A

   That applies 4% for all five years.

   C

   That applies 4% for three years and 6% for two, the wrong way round.

   D

   That applies 6% for all five years.

3. Question 3 of 5

   A nominal rate of 8% is compounded at different frequencies. Which gives the highest effective annual rate?

   Option A: Daily compoundingOption B: Half-yearly compoundingOption C: Quarterly compoundingOption D: Annual compounding

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   The answer is A: Daily compounding

   The more often interest is credited, the sooner it can be reinvested, so the effective rate rises with frequency: annual < half-yearly < quarterly < monthly < daily.

   Why the other options are wrong

   B

   More frequent compounding than half-yearly gives more.

   C

   Monthly and daily compounding give more than quarterly.

   D

   Annual compounding gives an effective rate equal to the nominal rate.

4. Question 4 of 5

   If interest rates rise, what happens to the present value of a fixed sum due in five years?

   Option A: It risesOption B: It becomes equal to the future valueOption C: It stays the sameOption D: It falls

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   The answer is D: It falls

   PV = FV ÷ (1 + r)ⁿ. A higher r makes the divisor larger, so the present value falls. This is why bond prices fall when interest rates rise.

   Why the other options are wrong

   A

   A higher rate means less needs investing now to reach the same sum.

   B

   That only happens at a zero rate.

   C

   The present value depends on the rate used.

5. Question 5 of 5

   A bond's theoretical price, found by discounting its cash flows, is £105.66. It trades in the market at £102.00. What might this suggest?

   Option A: The bond may be undervalued and worth buyingOption B: The bond is about to defaultOption C: The coupon must be below market ratesOption D: The bond is overvalued and should be sold

   Show answer

   The answer is A: The bond may be undervalued and worth buying

   Discounted cash flow analysis gives a fair value to compare with the traded price. A market price below the theoretical value suggests the investment may be undervalued.

   Why the other options are wrong

   B

   A price gap alone doesn't show default risk.

   C

   A theoretical price above par shows the opposite.

   D

   It trades below its theoretical value, not above.

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