Question:
Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6100
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8662
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 = $8662 – $6100 = $2562
Thus, Simple Interest = $2562
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 × 2562/6100 × 6
= 256200/36600
= 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) = $6100
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2562 (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 $6100
= 6/100 × 6100
= 6 × 6100/100
= 36600/100 = 366
Thus, simple Interest for 1 year = $366
Now,
∵ If the simple Interest is $366, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/366 years
∴ If the simple Interest is $2562, then the time = 1/366 × 2562 years
= 1 × 2562/366 years
= 2562/366 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.
(2) 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.
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.
(5) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 7 years.
(7) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.
(10) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.