Question

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 1

Answer:

The smallest amount to the nearest pound she can invest is £6,911

Step-by-step explanation:

Let

x -----> amount of money to be invested  

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  

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

substitute in the formula above  

$x(1+\frac{0.05}{1})^{1*3}> 8,000$  

$x(1.05)^{3}> 8,000$  

$x> 8,000/(1.05)^{3}$  

$x> \£6,910.70$  

therefore

The smallest amount to the nearest pound she can invest is £6,911