On the 1st of January 2014, Carol invested some money in a bank account. The account pays 2.5% compound interest per year. On the 1st of January 2015, Carol withdrew £1000 from the account. On the 1st of January 2016, she had £23 517.60 in the account. Work out how much Carol originally invested in the account?

Question

Frank Sexton

Mathematics

22 January, 15:29

On the 1st of January 2014, Carol invested some money in a bank account. The account pays 2.5% compound interest per year. On the 1st of January 2015, Carol withdrew £1000 from the account. On the 1st of January 2016, she had £23 517.60 in the account. Work out how much Carol originally invested in the account?

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Genesis Hammond · Answer 1

She started with x.

After 1 year, she had 1.025x.

She withdrew £1000, so now she has 1.025x - 1000.

Then it earned interest for 1 year and ended up as 1.025 (1.025x - 1000).

The actual amount of money was £23 517.60.

Therefore,

1.025 (1.025x - 1000) = 23517.60

1.025x - 1000 = 22 944

1.025x = 23 944

x = 23 360

Her original deposit was £23 360