Question:
Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10317
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 = $10317 – $5700 = $4617
Thus, Simple Interest = $4617
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 × 4617/5700 × 9
= 461700/51300
= 9 years (using formula)
Thus, Time (T) = 9 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) = $5700
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4617 (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 = 9% of Principal
= 9% of $5700
= 9/100 × 5700
= 9 × 5700/100
= 51300/100 = 513
Thus, simple Interest for 1 year = $513
Now,
∵ If the simple Interest is $513, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/513 years
∴ If the simple Interest is $4617, then the time = 1/513 × 4617 years
= 1 × 4617/513 years
= 4617/513 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?
(2) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 4 years.
(4) If Matthew paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 8 years.
(6) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.
(7) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?
(9) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(10) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.