Question

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 1

Answer:

The smallest amount is $\£6,911$

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

$A=P(1+\frac{r}{n})^{nt}$  

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  

$t=3\ years\\ A=\£8,000\\ r=5\%=5/100=0.05\\n=1$  

substitute in the formula above

$8,000=P(1+\frac{0.05}{1})^{1*3}$  

solve for P

$8,000=P(1.05)^{3}$  

$P=8,000/(1.05)^{3}$  

$P=\£6,910.70$  

Round to the nearest pound she can invest

The smallest amount is $\£6,911$