Question:
Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $10200
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 = $10200 – $6000 = $4200
Thus, Simple Interest = $4200
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 × 4200/6000 × 7
= 420000/42000
= 10 years (using formula)
Thus, Time (T) = 10 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) = $6000
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $4200 (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 = 7% of Principal
= 7% of $6000
= 7/100 × 6000
= 7 × 6000/100
= 42000/100 = 420
Thus, simple Interest for 1 year = $420
Now,
∵ If the simple Interest is $420, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/420 years
∴ If the simple Interest is $4200, then the time = 1/420 × 4200 years
= 1 × 4200/420 years
= 4200/420 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) If John paid $3456 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.
(3) If Barbara borrowed $3550 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.
(5) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11765 to clear the loan, then find the time period of the loan.
(6) Mary had to pay $3324.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(8) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 3 years.
(9) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 8 years.