SIMPLE INTEREST AND COMPOUND INTEREST

FIND THE RATE PERCENT PER ANNUM, IF RS. 2000 AMOUNTS TO RS. 2,315.25 IN A YEAR AND A HALF, INTEREST BEING COMPOUNDED HALF YEARLY.

 TIME = 3/2 years = 3 half years

RATE = 2R% per annum = R% for half year

 THEREFORE AMOUNT,

 = principal (1 + (Rate/100))^time

 2315.25 = 2000 (1 + (R/100))^3

231525/200000 = (1 + (R/100))^3

9261/8000 = (1 + (R/100))^3

(21/20)^3 = (1 + (R/100))^3

CANCELLING THE CUBE ON BOTH SIDES

21/20 = 1 + R/100

21/20 - 1 = R/100

1/20 = R/100\

R = 100/20

R = 5% per half year

THEREFORE REQUIRED RATE IS,

10% p. a.........

SIMPLE INTEREST ON A CERTAIN SUM OF MONEY FOR 3 YEARS AT 8% PER ANNUM IS HALF THE COMPOUND INTEREST ON RS 16000 FOR 2 YEARS AT 10% PER ANNUM. THE SUM PLACED ON THE SIMPLE INTEREST IS

 C.I  = P[(1 + R/100)^T - 1]

       = 16000[(1 + 10/100)^2 - 1]

       = 16000[(11/10)^2 - 1]

       = 16000[ 121/100 - 1]

       = 16000 * 21/100

       = RS 3360

THEREFORE,

 S.I. = 1/2 OF C.I.

SO, 

 P = (S.I. * 100 ) / R * T

P = 3360/2 * 100 *1/3 * 1/8

P = 1680 * 100 * 1/3 * 1/8

P = 560 * 100 * 1/8

P = 70 * 100

P = RS 7000

A WHOLESALER SELLS A WATCH TO A RETAILER AT A GAIN OF 32% AND THE RETAILER SELLS IT TO A CUSTOMER AT A  LOSS OF 20%. IF THE CUSTOMER PAYS RS 1953.6, WHAT HAD IT COST THE WHOLESALER?

 LET THE COST FOR WHOLESALER DEALER BE RS x

GAIN 32%  = 132/100

LOSS 20% = 80/100

ACCORDING TO THE QUESTION,

x * 132/100 * 80/100 = 1953.6

x = 1953.6 * 100/132 * 100/80

x = RS 1850

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