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] ...