Question:
Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $11040
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 = $11040 – $6900 = $4140
Thus, Simple Interest = $4140
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 × 4140/6900 × 10
= 414000/69000
= 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) = $6900
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4140 (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 $6900
= 10/100 × 6900
= 10 × 6900/100
= 69000/100 = 690
Thus, simple Interest for 1 year = $690
Now,
∵ If the simple Interest is $690, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/690 years
∴ If the simple Interest is $4140, then the time = 1/690 × 4140 years
= 1 × 4140/690 years
= 4140/690 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
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(2) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(3) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 3 years.
(5) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?
(7) If Robert borrowed $3100 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
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(9) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.
(10) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.