A sum of money amount to Rs 5200 in 5 year and to Rs5680 in 7years at ...
Calculation of simple interest:
Simple interest is calculated using the formula:
Simple Interest = (P * R * T) / 100
Where,
P = Principal amount
R = Rate of interest
T = Time in years
Calculation of principal amount:
Let the principal amount be P
According to the question,
P + (P * R * 5) / 100 = 5200
P + (5PR) / 100 = 5200
P + 0.05PR = 5200
Similarly,
P + (P * R * 7) / 100 = 5680
P + (7PR) / 100 = 5680
P + 0.07PR = 5680
Solving the equations:
Multiplying the first equation by 100 and subtracting it from the second equation, we get:
0.07PR - 0.05PR = 5680 - 5200
0.02PR = 480
PR = 24000
Therefore, the principal amount is Rs. 24000.
Calculation of rate of interest:
Using the first equation and substituting the value of P, we get:
24000 + (24000 * R * 5) / 100 = 5200
24000R = 5200 - 12000
24000R = 4000
R = 4000 / 24000
R = 1/6
R = 0.1667
Therefore, the rate of interest is 16.67%.
Answer:
The simple interest per annum is 16.67%.
A sum of money amount to Rs 5200 in 5 year and to Rs5680 in 7years at ...
P + SI for 5 years = 5200…………(I) P + SI for 7 years = 5680…………(II) On subtracting equation (I) from (II) SI for 2 years = 480 ∴ SI for 1 years = 240 ∴ From equation (I), P + 5 \times 240 = 5200 => P = 5200 - 1200 = 4000 Rs. \therefore R = \frac{SI\times 100}{T\times P} = \frac{240\times 100}{1\times 4000} = 6\% thus, answer is 6%
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