Question:
Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $11524
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 = $11524 – $6700 = $4824
Thus, Simple Interest = $4824
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 × 4824/6700 × 9
= 482400/60300
= 8 years (using formula)
Thus, Time (T) = 8 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) = 9% per annum
Simple Interest = $4824 (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 $6700
= 9/100 × 6700
= 9 × 6700/100
= 60300/100 = 603
Thus, simple Interest for 1 year = $603
Now,
∵ If the simple Interest is $603, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/603 years
∴ If the simple Interest is $4824, then the time = 1/603 × 4824 years
= 1 × 4824/603 years
= 4824/603 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(3) How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?
(4) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.
(5) In how much time a principal of $3150 will amount to $3465 at a simple interest of 2% per annum?
(6) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.
(7) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.
(8) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(9) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(10) David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.