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A sum of money becomes Rs 35,280 after 2 years and Rs 37,044 after 3 years when lent on compound interest. Find the principal amount.
- a)2800
- b)3000
- c)3200
- d)4000
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A sum of money becomes Rs 35,280 after 2 years and Rs 37,044 after 3 y...
37044 = p*(1 +r/100)3
35280 = p*(1 + r/100)2
Divide both equations to get the value of r and then substitute in any equation to get P
35280 = p*(1 + r/100)2
Divide both equations to get the value of r and then substitute in any equation to get P
Most Upvoted Answer
A sum of money becomes Rs 35,280 after 2 years and Rs 37,044 after 3 y...
37044 = p*(1 +r/100)3
35280 = p*(1 + r/100)2
Divide both equations to get the value of r and then substitute in any equation to get P
35280 = p*(1 + r/100)2
Divide both equations to get the value of r and then substitute in any equation to get P
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A sum of money becomes Rs 35,280 after 2 years and Rs 37,044 after 3 y...
Problem: To find the principal amount, given the amount after 2 years and 3 years when lent on compound interest.
Solution: Let the principal be P and the rate of compound interest be r.
Amount after 2 years = Rs 35,280
Using the formula for compound interest, we have
A = P(1 + r/100)^n
where A is the amount, n is the number of years.
Substituting the values, we get
35,280 = P(1 + r/100)^2
Amount after 3 years = Rs 37,044
Similarly, we have
37,044 = P(1 + r/100)^3
Dividing the two equations, we get
35,280/37,044 = (1 + r/100)^2/(1 + r/100)^3
Simplifying, we get
0.95 = 1/(1 + r/100)
1 + r/100 = 1/0.95
r/100 = (1/0.95) - 1
r/100 = 0.0526
r = 5.26%
Substituting the value of r in either of the above equations, we can find the value of P.
Let's use the first equation for simplicity.
35,280 = P(1 + 5.26/100)^2
P = 35,280/(1.0526)^2
P = Rs 32,00
Therefore, the principal amount is Rs 32,00.
Hence, the correct answer is option (c) 3200.
Solution: Let the principal be P and the rate of compound interest be r.
Amount after 2 years = Rs 35,280
Using the formula for compound interest, we have
A = P(1 + r/100)^n
where A is the amount, n is the number of years.
Substituting the values, we get
35,280 = P(1 + r/100)^2
Amount after 3 years = Rs 37,044
Similarly, we have
37,044 = P(1 + r/100)^3
Dividing the two equations, we get
35,280/37,044 = (1 + r/100)^2/(1 + r/100)^3
Simplifying, we get
0.95 = 1/(1 + r/100)
1 + r/100 = 1/0.95
r/100 = (1/0.95) - 1
r/100 = 0.0526
r = 5.26%
Substituting the value of r in either of the above equations, we can find the value of P.
Let's use the first equation for simplicity.
35,280 = P(1 + 5.26/100)^2
P = 35,280/(1.0526)^2
P = Rs 32,00
Therefore, the principal amount is Rs 32,00.
Hence, the correct answer is option (c) 3200.
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