- Interest on Rs 1440 = Rs 216 for the third year
Compound Interest: Compound interest is the interest that is earned on the initial principal, plus all previously accumulated interest. It is calculated using the formula: A = P (1 + r/n) ^nt, where A is the total amount, P is the principal amount, r is the rate of interest per annum, t is the time in years and n is the number of times the interest is compounded in a year.
Given:
Manish earns an interest of Rs 1656 for the third year and Rs 1440 for the second year on the same sum.
We need to find the rate of interest if it is lent at compound interest.
To solve this problem, we can use the above formula for compound interest.
Let P = Principal Amount
Let r = Rate of interest
Let t1 = Time for which interest of Rs 1656 was earned
Let t2 = Time for which interest of Rs 1440 was earned
Now, we can write the equation as follows:
1656 = P (1 + r/n) ^n(t1)
1440 = P (1 + r/n) ^n(t2)
Subtracting the two equations, we have:
216 = P (1 + r/n) ^n(t1) - P (1 + r/n) ^n(t2)
Simplifying, we have:
216 = P (1 + r/n)^n(t1 - t2)
Since t1 - t2 = 1
216 = P (1 + r/n)^n
Dividing both sides by P, we have:
(1 + r/n)^n = 216/P
Taking log on both sides, we have:
n log (1 + r/n) = log (216/P)
Rearranging, we have:
r/n = (log (216/P))/n
Now, substituting the given values, we have:
r/n = (log (216/P))/n = (log (216/P))/3
Therefore, the rate of interest (r) = 3 (log (216/P))
Now, substituting the given values, we have:
r = 3 (log (216/P)) = 3 (log (216/1000)) = 3 (log (0.216))
Therefore, the rate of interest (r) = 3 (log (0.216)) = 3 (-1.67) = -5.01
Therefore, the rate of interest (r) = -5.01%
Therefore, the correct answer is Option C - 15.
If you think the solution is wrong then please provide your own solution below in the comments section .
- Interest on Rs. 100 for the year = Rs. 4 Interest on Rs. 100 for the second year = 100 ( 1+ 4 ) 2 - 1 100 - 4 = Rs. 4.16 Now if Rs. 4.16 - Rs. 4 = Rs. 0.16 is the difference then principal = Rs. 100 Now if Rs. 88 is the difference then principal = 100 x 88 = Rs. 55,000 16
Let the sum of money lent be "P". Then, the interest earned for the first year is given by P * 4/100 = 0.04P.
For the second year, the interest earned is given by P * (4/100)^2 = 0.00016P.
The difference in interest between the second and first year is given as Rs. 88. Therefore, we have:
0.00016P - 0.04P = 88
Simplifying the above equation, we get:
0.04P(1 - 0.04) = 88
0.96P = 88
P = 88/0.96 = 55000
Hence, the sum of money lent is Rs. 55000, which corresponds to option B.
In summary, the solution to the problem involves the following steps:
If you think the solution is wrong then please provide your own solution below in the comments section .
- S.I. on Rs 65000 @ 10% for years = 65000 x 10 x 3 = Rs 19500 100 C.I. on Rs 65000 @ 10% for 3 years = 65000 ( 1+ 10 100 ) 3 - 65000 = 65000 11 x 11 x 11 -10 x 10 x 10 1000
• Simple Interest: Interest calculated only on the principal amount or the initial sum of money borrowed or invested. It is calculated as the product of the principal amount, the interest rate and the time period.
Formula: SI = (P x R x T)/100
Where,
P = Principal amount
R = Rate of interest
T = Time period
• Compound Interest: Interest calculated on the principal amount and the interest generated in the previous periods. It is calculated as the sum of principal amount and interest on the principal amount for the specified period of time.
Formula: CI = P (1 + R/100)^T - P
Where,
P = Principal amount
R = Rate of interest
T = Time period
• In the given question, Vibhor borrows Rs 65,000 at 10% per annum simple interest for 3 years and lends it at 10% per annum compound interest for 3 years.
• The simple interest earned by Vibhor in 3 years = (65000 x 10 x 3)/100
= Rs 19,500
• The compound interest earned by Vibhor in 3 years = 65000 (1 + 10/100)^3 - 65000
= Rs 2015
• Thus, Vibhor’s gain after 3 years is Rs 2015.
Hence, the correct answer is Option D - 2015.
If you think the solution is wrong then please provide your own solution below in the comments section .
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