Question:
William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7100
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are givenFormual to Calculate Simple Interest when Principal and Amount are given
We know that, Amount (A) = Principal (P) + Simple Interest (SI)
⇒ Simple Interest (SI) = Amount – Principal
⇒ SI = $7100 – $5000 = $2100
Thus, Simple Interest = $2100
Calculation of the Time using forumula when Amount, Simple Interest and Principal are known
Formula to find the Time (T)
Time (T) = 100 × Simple Interest/Principal × Rate of Interest
⇒ T = 100 × SI/P × R
Thus, Time (T) = 100 × 2100/5000 × 6
= 210000/30000
= 7 years (using formula)
Thus, Time (T) = 7 years (from time taken before calculation)Answer
Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known
Here, we have
Principal (P) = $5000
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2100 (As calculated above by subtracting Principal from the Amount given)
We know that, interest is calculated on the basis of the Principal.
This means Simple Interest for 1 year = Rate of simple interest × Principal
Thus, Simple Interest for 1 year = 6% of Principal
= 6% of $5000
= 6/100 × 5000
= 6 × 5000/100
= 30000/100 = 300
Thus, simple Interest for 1 year = $300
Now,
∵ If the simple Interest is $300, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/300 years
∴ If the simple Interest is $2100, then the time = 1/300 × 2100 years
= 1 × 2100/300 years
= 2100/300 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.
(2) If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.
(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(5) Susan had to pay $4197.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.
(8) If David borrowed $3400 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 6% simple interest?
(10) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.