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?
PLEASE SHOW WORKING OUT. THANKYOU.
23360 someone else told me i dont know how
To find out the original amount Carol invested in the account, we need to work backwards in time.
Let's start with the amount she had on the 1st of January 2016, which is £23,517.60.
To calculate how much she had on the 1st of January 2015, we need to subtract the interest she earned in 2015.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal/investment amount
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, we know the future value (A) is £23,517.60, the interest rate (r) is 2.5% (or 0.025 as a decimal), the number of compounding periods (n) is 1 per year, and the number of years (t) is 1.
So, the formula becomes:
£23,517.60 = P(1 + 0.025/1)^(1*1)
Simplifying the equation:
£23,517.60 = P(1 + 0.025)
Next, we need to find the amount on the 2nd of January 2014, which is before the withdrawal of £1000. To do that, we subtract the withdrawal amount from the amount on the 1st of January 2015.
£23,517.60 - £1000 = £22,517.60
We can now use this amount to calculate the original investment amount on the 1st of January 2014.
£22,517.60 = P(1 + 0.025)
Now, we can solve for P by dividing both sides of the equation by (1 + 0.025):
£22,517.60 / (1 + 0.025) = P
Calculating this on a calculator:
£22,517.60 / 1.025 ≈ £21,967.56
Therefore, Carol originally invested approximately £21,967.56 in the bank account.