Question:
William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $8000
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 = $8000 – $5000 = $3000
Thus, Simple Interest = $3000
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 × 3000/5000 × 10
= 300000/50000
= 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) = $5000
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $3000 (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 $5000
= 10/100 × 5000
= 10 × 5000/100
= 50000/100 = 500
Thus, simple Interest for 1 year = $500
Now,
∵ If the simple Interest is $500, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/500 years
∴ If the simple Interest is $3000, then the time = 1/500 × 3000 years
= 1 × 3000/500 years
= 3000/500 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?
(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 9% simple interest?
(3) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(5) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 4 years.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 8 years.
(7) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(8) Linda had to pay $3752 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(10) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.