Question:
Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6800
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $11084
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 = $11084 – $6800 = $4284
Thus, Simple Interest = $4284
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 × 4284/6800 × 7
= 428400/47600
= 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) = $6800
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $4284 (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 = 7% of Principal
= 7% of $6800
= 7/100 × 6800
= 7 × 6800/100
= 47600/100 = 476
Thus, simple Interest for 1 year = $476
Now,
∵ If the simple Interest is $476, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/476 years
∴ If the simple Interest is $4284, then the time = 1/476 × 4284 years
= 1 × 4284/476 years
= 4284/476 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
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(2) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.
(4) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.
(5) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
(7) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
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(9) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 7% simple interest.
(10) How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?