simple interest and compound interest

Question

A certain sum of money at simple interest amounts to $1768 in T years and to 1832 in T+4 years .If rate percent is not more than the sum ,then which of the following could be the rate percent.

(a)5
(b)20
(c)32
(d)40
(e)50

Answer 1

Okay I will give it a shot. I must admit I find the wording of the problem a bit confusing. 

 

the formula for simple interest compounded once a year gives

 

1765 = P(1+x)^T where x is the unknown interest rate

The problem also tells us that

1832 = P(1+x)^(T+4) = P(1+x)^T * (1+x)^4 are you following?

 

So 1832 = 1765 * (1+x)^4

 

(1832/1765) = (1+x)^4 = 1.038

 

Take the 4th root of both sides

 

1+x = 1.009368 or an interest rate of 0.9 percent which is not one of the choices