Theo put £350 into a savings account which gathered simple interest at a rate of 2% per month.
After 6 months, Theo used some money in the account to buy a bike costing £360.
How much money did Theo have left?
After the first month, Theo's savings account would have grown by 2% of £350, which is £7. This means he would have £350 + £7 = £357 in the account after one month.
After the second month, his savings would have grown by another 2%, which is 2% of £357, or £7.14, giving him a total of £364.14 in the account.
Repeating this process for all 6 months, we can calculate that Theo would have had £376.23 in the account at the end of the 6 months if he hadn't withdrawn any money to buy the bike.
Since he did spend £360 on the bike, we can subtract this from his total savings:
£376.23 - £360 = £16.23
Therefore, Theo had £16.23 left in his savings account after buying the bike.
To calculate the amount of money Theo has left after 6 months, we need to find the total amount of interest earned on the initial deposit of £350.
Step 1: Calculate the monthly interest
The monthly interest rate is 2%. To find the monthly interest, we can use the formula:
Monthly interest = (Interest rate/100) x Principal amount
Monthly interest = (2/100) x £350
Calculating this:
Monthly interest = (2/100) x £350
= (2/100) x £350
= 2/100 x £350
= £7
Step 2: Calculate the total interest earned after 6 months
Since the interest is compounded monthly, we need to multiply the monthly interest by the number of months:
Total interest earned after 6 months = Monthly interest x Number of months
Total interest earned after 6 months = £7 x 6
= £42
Step 3: Calculate the total amount after 6 months
Total amount after 6 months = Principal amount + Total interest earned
Total amount after 6 months = £350 + £42
= £392
Step 4: Calculate the amount of money left after buying the bike
After buying the bike, Theo has £360 left.
Amount of money left = Total amount after 6 months - Cost of bike
Amount of money left = £392 - £360
= £32
Therefore, Theo has £32 left in his savings account.