Question:
Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $9617
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 = $9617 – $5900 = $3717
Thus, Simple Interest = $3717
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 × 3717/5900 × 9
= 371700/53100
= 7 years (using formula)
Thus, Time (T) = 7 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) = $5900
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3717 (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 $5900
= 9/100 × 5900
= 9 × 5900/100
= 53100/100 = 531
Thus, simple Interest for 1 year = $531
Now,
∵ If the simple Interest is $531, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/531 years
∴ If the simple Interest is $3717, then the time = 1/531 × 3717 years
= 1 × 3717/531 years
= 3717/531 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.
(3) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(4) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(5) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.
(6) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.
(8) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(10) How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?