Cynthia invests some money in a bank which pays 5% compound interest per year she wants it to be over 8000 at the end of three years what is the smallest amount to the nearest pound she can invest

Answer:The smallest amount to the nearest pound she can invest is £6,911Step-by-step explanation:Letx -----> amount of money to be invested  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\\ P=x\\r=5\%=5\100=0.05\\n=1\\A>\£8,000[/tex]  substitute in the formula above  [tex]x(1+\frac{0.05}{1})^{1*3}> 8,000[/tex]  [tex]x(1.05)^{3}> 8,000[/tex]  [tex]x> 8,000/(1.05)^{3}[/tex]  [tex]x> \£6,910.70[/tex]  thereforeThe smallest amount to the nearest pound she can invest is £6,911