Question:
Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6400
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $11584
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 = $11584 – $6400 = $5184
Thus, Simple Interest = $5184
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 × 5184/6400 × 9
= 518400/57600
= 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) = $6400
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $5184 (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 = 9% of Principal
= 9% of $6400
= 9/100 × 6400
= 9 × 6400/100
= 57600/100 = 576
Thus, simple Interest for 1 year = $576
Now,
∵ If the simple Interest is $576, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/576 years
∴ If the simple Interest is $5184, then the time = 1/576 × 5184 years
= 1 × 5184/576 years
= 5184/576 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
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(2) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 8 years.
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(7) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(8) If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
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