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
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(2) How much loan did Joshua borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8625 to clear it?
(3) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.
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(7) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?
(8) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
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