A company invests £5000 in a maintenance fund that earns compound interest at 3.5% per year. Work out how much the fund is worth after 4 years, giving your ...
Question 1 Report
A company invests £5000 in a maintenance fund that earns compound interest at 3.5% per year.
- Work out how much the fund is worth after 4 years, giving your answer to the nearest penny. (3)
- State how much interest the investment has earned over this time. (1)
- A rival scheme offers simple interest at 4% per year on the same £5000 over 4 years. Work out the value of this scheme after 4 years. (2)
- State which scheme gives the greater return after 4 years, and by how much. (2)
- Explain why, even though compound interest is usually described as growing faster than simple interest, the simple interest scheme gives the better return here. (4)
Answer Details
This question again compares compound and simple interest, this time asking why the type of growth normally described as faster, compound interest, actually gives the smaller return over this particular period.
(a) Compound interest after 4 years at 3.5%:
\[ £5000 \times 1.035^4 = £5000 \times 1.147523 = £5737.62 \](correct to the nearest penny) [3]
(b) Interest earned:
\[ £5737.62 - £5000 = £737.62 \][1]
(c) Simple interest at 4% over 4 years:
\[ £5000 \times 0.04 \times 4 = £800, \quad \text{value} = £5000 + £800 = £5800 \][2]
(d) Comparing the two schemes:
\[ £5800 - £5737.62 = £62.38 \]The simple interest scheme gives the greater return after 4 years, by £62.38. [2]
(e) Compound interest only overtakes a given simple interest rate once the compound rate and the elapsed time are large enough for the repeated compounding to make up the gap between the two rates. Here the compound rate, 3.5%, is already lower than the simple rate, 4%, so compound interest starts behind; four years is not long enough for compounding on the smaller rate to close that gap and pull ahead. [4]
This shows that "compound interest grows faster" is only true in the long run and only once its own rate is being compared fairly; a lower compound rate can lose to a higher simple rate for many years, exactly as it does here.
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