Ramdeen purchased rahat patras for rs 1000 a sum which will fetch him rs 2000 after 5 year find rate of interest if the interest is compounded half years
Answers
Answer:
Rate of interest = 14.35 per cent per year
Step-by-step explanation:
P = principal amount = 1000
R = rate of interest per cent per year
T = number of years = 5
m = compounding interval = 2 (six-monthly compounding)
A = final amount = 2000
A = P(1 + (R/m)/100)^Tm
Substituting the various values,
2000 = 1000*(1 + (R/2)/100)^10
2 = (1+(R/2)/100)^10
(1 + (R/2)/100) = 2^(1/10)
(R/2)/100 = 2^(1/10) - 1
R/2 = 100*[2^(1/10) - 1]
R = 200*[2^(1/10) - 1]
R = 14.35
Rate of interest = R = 14.35 per cent per year
Note: 2^(1/10) is the tenth root of 2 and has been found out using a calculator!
2^(`1/10) = 1.071773
Answer:
Rate of interest = 14.35 per cent per year
Step-by-step explanation:
P = principal amount = 1000
R = rate of interest per cent per year
T= number of years = 5
m = compounding interval = 2
(six-monthly compounding)
A final amount = 2000
A = P(1 + (R/m)/100)^Tm
Substituting the various values,
2000=1000*(1+ (R/2)/100)^10
2 = (1+(R/2)/100)^10
+ (R/2)/100) = 2^(1/10)
(R/2)/100 = 2^(1/10) - 1
R/2 = 100*[2^(1/10) - 1]
Rate of interest = R = 14.35 per cent per year
Note: 2^(1/10) is the tenth root of 2 and has
been found out using a calculator!
2^(1/10)=1.071773