Compound intrest

Question

On the 1st January 2014 Carol invested some money in a bank account.
The account pays 2.5% compound interest per year.
On the 1st January 2015 Carol withdrew £1000 from the account.
On the 1st January 2016 she had £23517.60 in the account.

Work out how much carol originally invested in the account.

Answer 1

Because of the withdrawal on 01/01/2015, we have to break this down into 2 distinct calculations:

 

PV = (23,517.60)/1.025 = 22,944 Pounds Sterling

 

Then, we add back the 1,000 Pounds Sterling that was withdrawn exactly 1 year prior, to get:  23,944 Pounds Sterling

 

Carol had deposited the annual interest for exactly 1 year (2.5%) less than the value of 23,944 Pounds Sterling

 

So:  PV (of 01/01/2014) is:  (23,944/1.025) = 23,360

 

So, on 01/01/2014, Carol initially deposit 23,360 Pounds Sterling into a bank account earning 2.5% APR.