I = prt = [15000 × 0.07 × (214/365) ]=615.52

Future value, S = P + I = $15 000 + $615.52 = $15 615.52

t=I/pr

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

P = F 1 + i n

Let the sum be Rs. x

a. gives, S.I = Rs. 9000 and time = 9 years.

b. gives, Sum + S.I for 6 years = 2 x Sum

--> Sum = S.I for 6 years.

Now, S.I for 9 years = Rs. 9000

S.I for 1 year = Rs. 9000/9 = Rs. 1000.

S.I for 6 years = Rs. (1000 x 6)= Rs. 6000.

--> x = Rs. 6000

Thus, both a and b are necessary to answer the question.

Let the principle be Rs. P
As the amount double itself the interest is Rs. P too
So P = P x r x 15/100
=> r = 100/15 = 20/3 % = 6.66 %.

Let Althaf lent Rs. A at 14% per year.
Hence, Money lent at 12% = (1500-A);
Given, total interest = Rs. 186.
{(A x 14x 1)/100} + {[(1500-A) x 12 x 1/100]} = 186;
14A/100 + (18000 -12A)/100 = 186;
14A + 18000 - 12A = 186x100;
2A = 18600-18000;
A = 600/2 = Rs. 300.
Hence, money lent at 12% = 1500-300 = Rs. 1200.

Rate = 4%

Time = 8 years

Simple Interest = PTR/100

= 32P/100

Given, P ?32P/100 = 34068

P = 34000

P = 500

Let the rate of interest be R

(Interest at rate (R+4)%)?(Interest at R%)

= 600(PT(R+4)/100) ?(PTR/100)

= 6003PR +12P ?3PR = 60000

12P = 60000

P = 5000