Question:
Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9112 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9112
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 = $9112 – $6700 = $2412
Thus, Simple Interest = $2412
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 × 2412/6700 × 6
= 241200/40200
= 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) = $6700
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2412 (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 = 6% of Principal
= 6% of $6700
= 6/100 × 6700
= 6 × 6700/100
= 40200/100 = 402
Thus, simple Interest for 1 year = $402
Now,
∵ If the simple Interest is $402, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/402 years
∴ If the simple Interest is $2412, then the time = 1/402 × 2412 years
= 1 × 2412/402 years
= 2412/402 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
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(2) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
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(6) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
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