Chapter 8, Problem 4STP

To determine

To find: the time taken by J to get $2750 in her account

Answer to Problem 4STP

The correct option is: H

Explanation of Solution

Given:

J invest $2000

He earns interest of 7.5%.

The amount she receives after some time is $2750.

F 10 years

H 5 years

G 8 years

J 4 years

Formula used:

The simple interest is calculated by

  $SI=\frac{P\times R\times T}{100}$

Calculation:

Now, in order to calculate time taken by Janelle to earn $2750, first calculate the simple interest earn by Janelle.

As, principal is $2000 and amount is $2750

Since, the simple interest is difference between principal and amount. It means that the value of simple interest is $750.

Now, the formula to calculate the simple interest is:

  $SI=\frac{P\times R\times T}{100}$

Thus,

  $750=\frac{2000\times 7.50\times T}{100}$

Simplify.

  $750=20\times 7.50\times T$

Remove the decimal.

  $750=\frac{20\times 750\times T}{100}$

Cancel 750 from both sides of equation.

  $1=\frac{20\times T}{100}$

Cross multiply the equation.

  $100=20\times T$

Divide the equation by 20.

  $\begin{array}{c}\frac{100}{20}=\frac{20\times T}{20}\\ 5=T\end{array}$

Hence, the time taken by Janelle to get $2750 in her account is 5 years.

Conclusion:

Therefore, the correct option is: H