Question:
Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $10620
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 = $10620 – $5900 = $4720
Thus, Simple Interest = $4720
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 × 4720/5900 × 10
= 472000/59000
= 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) = $5900
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4720 (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 = 10% of Principal
= 10% of $5900
= 10/100 × 5900
= 10 × 5900/100
= 59000/100 = 590
Thus, simple Interest for 1 year = $590
Now,
∵ If the simple Interest is $590, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/590 years
∴ If the simple Interest is $4720, then the time = 1/590 × 4720 years
= 1 × 4720/590 years
= 4720/590 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) If Linda paid $3752 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 7 years.
(5) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 4 years.
(7) If William borrowed $3500 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(8) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
(10) If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.