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A sum of money, at compound interest, yields Rs. 200 and Rs. 220 at the end of first and second years respectively. What is the rate percent?
- a)20%
- b)15%
- c)10%
- d)5%
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A sum of money, at compound interest, yields Rs. 200 and Rs. 220 at th...
To find the rate of interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount
r = Rate of interest
n = Number of times interest is compounded per year
t = Time in years
Given that the amount at the end of the first year is Rs. 200 and the amount at the end of the second year is Rs. 220, we can set up two equations using the compound interest formula.
Equation 1:
200 = P(1 + r/n)^(nt)
Equation 2:
220 = P(1 + r/n)^(2nt)
Now we need to solve these equations to find the value of r (rate of interest).
Solving the first equation for P, we get:
P = 200 / (1 + r/n)^(nt)
Substituting this value of P into the second equation, we get:
220 = (200 / (1 + r/n)^(nt))(1 + r/n)^(2nt)
Simplifying the equation, we get:
220 = 200(1 + r/n)^(nt)(1 + r/n)^(nt)
Dividing both sides by 200, we get:
11/10 = (1 + r/n)^(nt)
Taking the nth root of both sides, we get:
(11/10)^(1/nt) = 1 + r/n
Subtracting 1 from both sides, we get:
(11/10)^(1/nt) - 1 = r/n
Multiplying both sides by n, we get:
n((11/10)^(1/nt) - 1) = r
Now we can substitute the given values to find the rate of interest.
Given:
n = 1 (compounded annually)
t = 2 (two years)
220 = 200(1 + r/1)^(1*2)
Simplifying the equation, we get:
11/10 = (1 + r)^(2)
Taking the square root of both sides, we get:
√(11/10) = 1 + r
Subtracting 1 from both sides, we get:
√(11/10) - 1 = r
Converting this to a percentage, we get:
r ≈ 0.0488 or 4.88%
Therefore, the rate of interest is approximately 4.88%, which is closest to option C) 10%.
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount
r = Rate of interest
n = Number of times interest is compounded per year
t = Time in years
Given that the amount at the end of the first year is Rs. 200 and the amount at the end of the second year is Rs. 220, we can set up two equations using the compound interest formula.
Equation 1:
200 = P(1 + r/n)^(nt)
Equation 2:
220 = P(1 + r/n)^(2nt)
Now we need to solve these equations to find the value of r (rate of interest).
Solving the first equation for P, we get:
P = 200 / (1 + r/n)^(nt)
Substituting this value of P into the second equation, we get:
220 = (200 / (1 + r/n)^(nt))(1 + r/n)^(2nt)
Simplifying the equation, we get:
220 = 200(1 + r/n)^(nt)(1 + r/n)^(nt)
Dividing both sides by 200, we get:
11/10 = (1 + r/n)^(nt)
Taking the nth root of both sides, we get:
(11/10)^(1/nt) = 1 + r/n
Subtracting 1 from both sides, we get:
(11/10)^(1/nt) - 1 = r/n
Multiplying both sides by n, we get:
n((11/10)^(1/nt) - 1) = r
Now we can substitute the given values to find the rate of interest.
Given:
n = 1 (compounded annually)
t = 2 (two years)
220 = 200(1 + r/1)^(1*2)
Simplifying the equation, we get:
11/10 = (1 + r)^(2)
Taking the square root of both sides, we get:
√(11/10) = 1 + r
Subtracting 1 from both sides, we get:
√(11/10) - 1 = r
Converting this to a percentage, we get:
r ≈ 0.0488 or 4.88%
Therefore, the rate of interest is approximately 4.88%, which is closest to option C) 10%.
Community Answer
A sum of money, at compound interest, yields Rs. 200 and Rs. 220 at th...
20%
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