Cynthia invests some money in a bank which pays 5% compound interest per year. She wants it to be worth over £8000 at the end of 3 years. What is the smallest amount, to the nearest pound, she can invest?

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 investThe smallest amount is [tex]\£6,911[/tex]