Question:
James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $7200
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 = $7200 – $4000 = $3200
Thus, Simple Interest = $3200
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 × 3200/4000 × 10
= 320000/40000
= 8 years (using formula)
Thus, Time (T) = 8 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) = $4000
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $3200 (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 = 10% of Principal
= 10% of $4000
= 10/100 × 4000
= 10 × 4000/100
= 40000/100 = 400
Thus, simple Interest for 1 year = $400
Now,
∵ If the simple Interest is $400, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/400 years
∴ If the simple Interest is $3200, then the time = 1/400 × 3200 years
= 1 × 3200/400 years
= 3200/400 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount does James have to pay after 6 years if he takes a loan of $3000 at 7% simple interest?
(2) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?
(4) If William paid $4060 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 7% simple interest?
(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 7 years.
(7) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
(9) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 3% simple interest.