Question:
Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $8640
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 = $8640 – $5400 = $3240
Thus, Simple Interest = $3240
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 × 3240/5400 × 10
= 324000/54000
= 6 years (using formula)
Thus, Time (T) = 6 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) = $5400
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $3240 (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 $5400
= 10/100 × 5400
= 10 × 5400/100
= 54000/100 = 540
Thus, simple Interest for 1 year = $540
Now,
∵ If the simple Interest is $540, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/540 years
∴ If the simple Interest is $3240, then the time = 1/540 × 3240 years
= 1 × 3240/540 years
= 3240/540 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3410 at a simple interest of 5% per annum?
(2) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.
(4) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(7) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?
(8) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.
(10) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.