Question:
Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $8639
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 = $8639 – $5300 = $3339
Thus, Simple Interest = $3339
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 × 3339/5300 × 7
= 333900/37100
= 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) = $5300
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3339 (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 $5300
= 7/100 × 5300
= 7 × 5300/100
= 37100/100 = 371
Thus, simple Interest for 1 year = $371
Now,
∵ If the simple Interest is $371, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/371 years
∴ If the simple Interest is $3339, then the time = 1/371 × 3339 years
= 1 × 3339/371 years
= 3339/371 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.
(3) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?
(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 8 years.
(6) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?
(7) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 4 years.
(9) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.
(10) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.