Question

The amount of simple interest accrued on a sum of money varies jointly with the amount of money, the interest rate, and the time the money is invested. A sum of money is invested at 4% for 3 years and accrues $168 in interest. The same sum of money is invested in a second account at 6% for 4 years. Which statement is true?

A. The amount of interest accrued on the second account is less than double the amount of interest accrued on the first account.
B. The amount of interest accrued on the second account is double the amount of interest accrued on the first account.
C. The amount of interest accrued on the second account is more than double but less than triple the interest on the first account.
D. The amount of interest accrued on the second account is more than triple the interest accrued on the first account.

Answer 1

Find the amount of the first one
P=168/0.04*3
P=1400
Use the in the second one to find the interest
I=1400*0.06*4
I=336
336 is double the amount of 168
So the answer is B

Answer 2

Option (B) is correct i.e the amount of interest accrued on the second account is double the amount of interest accrued on the first account.

Explanation:

As given

The amount of simple interest accrued on a sum of money varies jointly with the amount of money, the interest rate, and the time the money is invested.

Thus

Formula for simple interest .

`Simple\ interest = (Principle* Rate* Time )/(100)`

As given

A sum of money is invested at 4% for 3 years and accrues $168 in interest.

Put in the above

`168 = (Principle* 4* 3)/(100)`

`Principle = (16800)/(12)`

Principle = $1400

As given

The same sum of money is invested in a second account at 6% for 4 years.

Put in the formula

`Simple\ interest = (1400* 6* 4)/(100)`

`Simple\ interest = (33600)/(100)`

Simple interest = $336

Thus Option (B) is correct i.e the amount of interest accrued on the second account is double the amount of interest accrued on the first account.