Question:
Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9860
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 = $9860 – $5800 = $4060
Thus, Simple Interest = $4060
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 × 4060/5800 × 7
= 406000/40600
= 10 years (using formula)
Thus, Time (T) = 10 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) = $5800
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $4060 (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 $5800
= 7/100 × 5800
= 7 × 5800/100
= 40600/100 = 406
Thus, simple Interest for 1 year = $406
Now,
∵ If the simple Interest is $406, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/406 years
∴ If the simple Interest is $4060, then the time = 1/406 × 4060 years
= 1 × 4060/406 years
= 4060/406 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(3) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?
(4) Joseph had to pay $4033 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(7) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?
(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.
(9) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.