A certain principal amount to RS 560 in 3 years and rs600 in 5 years. Determine the rate of interest per annum
Answers
The rate of interest is 4% p.a.
Step-by-step explanation:
Formula Used:
- Simple interest, S.I. = Amount – Principal = [PRT] / 100
Let the rate of interest be denoted as “R”%.
According to the question and based on the formula we can write the eq. as,
Equation 1:
560 – P = [PR*3]/100
Equation 2:
600 – P = [PR*5]/100
⇒ 60000 – 100P = 5PR
⇒ [60000 – 100P] = 5/3 * [56000 – 100P] …… [substituting from (i)]
⇒ 3*[60000 – 100P] = 5*[56000 – 100P]
⇒ 180000 – 300P = 280000 – 500P
⇒ 500P – 300P = 280000 – 180000
⇒ 200P = 100000
⇒ P = Rs. 500
Substituting the value of P in eq. (i), we get
1/3 * [56000 – 100P] = PR
⇒ [56000 – (100* 500)] = 3* 500*R
⇒ 56000 – 50000 = 1500R
⇒ 1500R = 6000
⇒ R = 60/15
⇒ R = 4% p.a. ← rate of interest per annum
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Rate of interest = 4%
Step-by-step explanation:
Interest in 3 years = Rs. 560
Interest in 5 years = Rs. 600
Interest in 2 years = 600 - 560 = Rs. 40
Interest in 1 year = 40 / 2 = Rs. 20
So interest in 3 years = 20 * 3 = Rs. 60
Principal = 560 - 60 = Rs. 500
SI = PNR / 100
20 = 500 * 1 * R / 100
R = 2000 / 500
R = 4%