Question:
Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $8378
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 = $8378 – $5900 = $2478
Thus, Simple Interest = $2478
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 × 2478/5900 × 7
= 247800/41300
= 6 years (using formula)
Thus, Time (T) = 6 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) = 7% per annum
Simple Interest = $2478 (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 = 7% of Principal
= 7% of $5900
= 7/100 × 5900
= 7 × 5900/100
= 41300/100 = 413
Thus, simple Interest for 1 year = $413
Now,
∵ If the simple Interest is $413, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/413 years
∴ If the simple Interest is $2478, then the time = 1/413 × 2478 years
= 1 × 2478/413 years
= 2478/413 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(2) If Sandra paid $4984 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?
(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 2% simple interest?
(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(7) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 3 years.
(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.