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A sum of Rs. 10 is lend to be returned in 11 monthly instalments of Rs. 1 each, interest being simple. The rate of interest charged is:
- a)10%
- b)22%
- c)
- d)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A sum of Rs. 10 is lend to be returned in 11 monthly instalments of Rs...
Given :
A sum of Rs. 10 is lend to be returned in 11 monthly instalments of Rs . 1 each interest being simple
Formula used :
Simple interest = P × R× T /100
Principal(P), Rate(R) and Time(T)
Calculation :
Let the rate of interest be R% per annum
⇒ Amount to be paid (if paid at the end of 11 months)
⇒ 10 + [10 × R × (11/12) / 100] = 10 + (11R/120)
⇒ Total effective payment = (Rs. 1 + interest on Rs. 1 for 10 months) + (Rs. 1 + interest on Rs. 1 for 9 months) + .... +(Rs. 1 + interest on Rs. 1 for 1 months) + Rs. 1
⇒ (1 + 1 × R × (10/12) / 100) + (1 + 1 × R × (9/12) / 100) + .... + (1 + 1 × R × (1/12) / 100) + 1
⇒ (1 + 10R/1200) + (1 + 9R/1200) + .... + (1 + R/1200) + 1
⇒ 11 + R(1 + 2 + .... + 10)/1200
⇒ 11 + R(10 × 11 / 2)/1200
⇒ 11 + R(10 × 11 / 2)/1200
⇒ 11 + 11R/240
Now we have,
⇒ 10 + 11R/120 = 11 + 11R/240
⇒ 11R/240 = 1
⇒ R = 240/11 = 21× 9/11%
∴ Rate of interest is 21(9/11)%
Most Upvoted Answer
A sum of Rs. 10 is lend to be returned in 11 monthly instalments of Rs...
Given:
Principal (P) = Rs. 10
Number of installments (n) = 6
Amount of each installment (A) = Rs. 3
To find: Rate of interest (R)
Formula used:
Simple Interest (SI) = PNR/100
Total amount to be repaid = A x n = 3 x 6 = Rs. 18
Total interest paid = Total amount to be repaid - Principal = 18 - 10 = Rs. 8
Calculation:
SI = PNR/100
8 = 10 x N x R/100
N x R = 80
Rate of interest (R) = (N x R/P) x 100
R = (80/10) x 100/6
R = 640/6
R = 106.67%
Therefore, the rate of interest is 640%.
Principal (P) = Rs. 10
Number of installments (n) = 6
Amount of each installment (A) = Rs. 3
To find: Rate of interest (R)
Formula used:
Simple Interest (SI) = PNR/100
Total amount to be repaid = A x n = 3 x 6 = Rs. 18
Total interest paid = Total amount to be repaid - Principal = 18 - 10 = Rs. 8
Calculation:
SI = PNR/100
8 = 10 x N x R/100
N x R = 80
Rate of interest (R) = (N x R/P) x 100
R = (80/10) x 100/6
R = 640/6
R = 106.67%
Therefore, the rate of interest is 640%.
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A sum of Rs. 10 is lend to be returned in 11 monthly instalments of Rs. 1 each, interest being simple. The rate of interest charged is:a)10%b)22%c)d)Correct answer is option 'D'. Can you explain this answer?
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