Simple Interest Questions

Let the Time be 'N' and Rate be 'R' 

J = (K x NR)/100 K = (L x NR)/100 

J/K = NR/100 K/L = NR/100 

J/K = K/L 

K x K = JL

Suppose the merchant will take advantage of the cash discount of 4% of $20 000 = $800 by paying the bill within 30 days from the date of invoice. He needs to borrow $20 000 = $800 = $19 200. He would borrow this money on day 30 and repay it on day 100 (the day the original invoice is due) resulting in a 70-day loan. The interest he should be willing to pay on borrowed money should not exceed the cash discount $800.

r=I/pt=21.73%

The highest simple interest rate at which the merchant can afford to borrow money is 21.73%. This is a break-even rate. If he can borrow money, say at a rate of 15%, he should do so. He would borrow $19 200 for 70 days at 15%. Maturity value of the loan is $19 200(1+0.15(70/365))=$19 752.33

savings would be $20 000 − $19 752.33 = $247.67

We know that I = PTR/100

11 = (2x30xR)/100

R = 18.333 %

I= PTR100

From the given data,

3500x7xt/100 = 500

=> t = 100/49 years

Now, in the second case

The interest per year = 49/100 x 800 = 392

 => 4900 x 1 x r/100 = 392

=> r = 8%

T = (100 x I)/ (P x r)

Let rate = R% and time = R years.

Then, (1200 x R x R) / 100 = 432

=> R = 6.

Let the amount at 6% be x
Amount at 10% be (10000 –x)
At 9.2 % interest, SI = 10000 X 9.2 X 1/100 = 920
Amount = 10920
⇒ 6x/100 + (10000 – x)10/100 = 920
⇒ 6x – 10x + 100000 = 92000
⇒ 4x = 8000
⇒ x = 2000
Money lent at 10 % = 10000 – 2000 = 8000