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

Therefore she can invest =5322.14 pound      

Step-by-step explanation:

Let ,Cynthia invested $x

Rate = 5%per year

time = 3 year

Amount $(A)= P(1+\frac{r}{100} )^t$

   $8000=x(1+\frac{5}{100})^3$

$\Leftrightarrow 8000=x(\frac{21}{20} )^3$

$\Leftrightarrow x=\frac{8000\times 8000}{9261}$  

$\Leftrightarrow x = 6910.7$

Therefore she can invest =$6910.7 =5322.14 pound      

                   

Answer 2

She can invest 6910.70 pound to make 8000.

Step-by-step explanation:

Let the principal amount that Cynthia could invest = x

Interest rate (r) = 5% = 0.05

time (t) = 3 years

n = number of compounding in a year (1)

Future amount =  >8000 pound

Formula for compound interest :

$A=P(1+\frac{r}{n})^{nt}$

$8000=x(1+\frac{0.05}{1})^{1\times3}$

8000 $=x(1+0.05)^3$

8000 = $x(1.05)^3$

8000 = 1.157625x

x = 6910.70

She could invest 6910.70 pound to make 8000.

Learn more about compound interest : https://brainly.in/question/8862893