Answer:
[tex]\large \boxed{\text{\pounds 23 360.00}}[/tex]
Step-by-step explanation:
The formula for the accrued amount from compound interest is
[tex]A = P \left(1 + \dfrac{r}{n}\right)^{nt}[/tex]
1. Amount in account on 1 Jan 2015
(a) Data:
a = £23 517.60
r = 2.5 %
n = 1
t = 1 yr
(b) Calculations:
r = 0.025
[tex]\begin{array}{rcl}23517.60 & = & P\left (1 + \dfrac{r}{n}\right)^{nt}\\\\& = & P\left (1 + \dfrac{0.025}{1}\right)^{1\times1}\\\\& = & P (1 + 0.025)\\ & = & 1.025 P\\P & = & \dfrac{23517.60 }{1.025} \\\\& = & 22 944.00 \\\end{array}[/tex]
The amount that gathered interest was £22 944.00 but, before the interest started accruing, Carol had withdrawn £1000 from the account.
She must have had £23 944 in her account on 1 Jan 2015.
(2) Amount originally invested
(a) Data
A = £23 944.00
[tex]\begin{array}{rcl}23 944.00 & = & 1.025 P\\P & = & \dfrac{23 944.00 }{1.025} \\\\& = & \mathbf{23 360.00} \\\end{array}\\\text{Carol originally invested $\large \boxed{\textbf{\pounds23 360.00}}$ in her account.}[/tex]
3. Summary
1 Jan 2014 P = £23 360.00
1 Jan 2015 A = 23 944.00
Withdrawal = -1 000.00
P = 22 944.00
1 Jan 2016 A = £23 517.60
