Question:
Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6800
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $12240
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 = $12240 – $6800 = $5440
Thus, Simple Interest = $5440
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 × 5440/6800 × 8
= 544000/54400
= 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) = $6800
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $5440 (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 = 8% of Principal
= 8% of $6800
= 8/100 × 6800
= 8 × 6800/100
= 54400/100 = 544
Thus, simple Interest for 1 year = $544
Now,
∵ If the simple Interest is $544, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/544 years
∴ If the simple Interest is $5440, then the time = 1/544 × 5440 years
= 1 × 5440/544 years
= 5440/544 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?
(3) If Elizabeth paid $4002 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?
(5) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(6) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?
(7) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(8) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?
(9) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(10) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.