Answer:
The smallest amount is [tex]\£6,911[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=3\ years\\ A=\£8,000\\ r=5\%=5/100=0.05\\n=1[/tex]
substitute in the formula above
[tex]8,000=P(1+\frac{0.05}{1})^{1*3}[/tex]
solve for P
[tex]8,000=P(1.05)^{3}[/tex]
[tex]P=8,000/(1.05)^{3}[/tex]
[tex]P=\£6,910.70[/tex]
Round to the nearest pound she can invest
The smallest amount is [tex]\£6,911[/tex]
