Question:
Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7854
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 = $7854 – $5100 = $2754
Thus, Simple Interest = $2754
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 × 2754/5100 × 6
= 275400/30600
= 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) = $5100
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2754 (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 = 6% of Principal
= 6% of $5100
= 6/100 × 5100
= 6 × 5100/100
= 30600/100 = 306
Thus, simple Interest for 1 year = $306
Now,
∵ If the simple Interest is $306, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/306 years
∴ If the simple Interest is $2754, then the time = 1/306 × 2754 years
= 1 × 2754/306 years
= 2754/306 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 3 years.
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.
(3) If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(5) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(6) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(8) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(9) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(10) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6392 to clear the loan, then find the time period of the loan.