Question

A bank account gathers compound interest at a rate of 5% each year.

Another bank account gathers the same amount of money in interest by
the end of each year, but gathers compound interest each month.
If Abraham puts £4300 into the account which gathers interest each
month, how much money would be in his account after 2 years and
5 months?
Give your answer in pounds to the nearest 1p.

Answer 1

£4838.11

Explanation:

You want the amount in an account after 2 years and 5 months if interest is compounded monthly with an effective rate of 5% per year. The beginning balance is £4300.

Effective rate

If the amount of interest earned from monthly compounding is identical to the amount earned by annual compounding, the effective monthly multiplier is ...

1.05^(1/12) ≈ 1.00407412

which is an effective monthly rate of 0.407412%, and an annual rate of 12 times that, about 4.88895%.

The balance after 29 months using the monthly rate of 0.407412% will be ...

£4300·1.00407412^29 ≈ £4838.11

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Additional comment

The key wording here is that the monthly compounding results in the same amount of interest being earned as for annual compounding at 5%. That is, the effective rate of the interest compounded monthly is 5% over a year's time.