Question

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?

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