On the 1st of January 2014, Carol invested some money in a bank account. The account pays 2.5% compound interest per year. On th
e 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?
She started with x. After 1 year, she had 1.025x. She withdrew <span>£1000, so now she has 1.025x - 1000. Then it earned interest for 1 year and ended up as </span>1.025(1.025x - 1000). The actual amount of money was £23 517.60. Therefore,
<span>1.025(1.025x - 1000) = 23517.60
1.025x - 1000 = 22 944
1.025x = 23 944
x = 23 360
Her original deposit was </span><span>£23 360</span>
