Question:
Mark took a loan of $6800 at the rate of 10% 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
8
Solution And Explanation
Solution
Given,
Principal (P) = $6800
Rate of Simple Interest (R) = 10% 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 × 10
= 544000/68000
= 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) = $6800
Rate of Simple Interest (R) = 10% 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 = 10% of Principal
= 10% of $6800
= 10/100 × 6800
= 10 × 6800/100
= 68000/100 = 680
Thus, simple Interest for 1 year = $680
Now,
∵ If the simple Interest is $680, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/680 years
∴ If the simple Interest is $5440, then the time = 1/680 × 5440 years
= 1 × 5440/680 years
= 5440/680 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.
(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.
(3) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?
(5) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.
(8) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 8 years.
(10) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.