Question:
William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9000
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 = $9000 – $5000 = $4000
Thus, Simple Interest = $4000
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 × 4000/5000 × 8
= 400000/40000
= 10 years (using formula)
Thus, Time (T) = 10 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) = 8% per annum
Simple Interest = $4000 (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 = 8% of Principal
= 8% of $5000
= 8/100 × 5000
= 8 × 5000/100
= 40000/100 = 400
Thus, simple Interest for 1 year = $400
Now,
∵ If the simple Interest is $400, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/400 years
∴ If the simple Interest is $4000, then the time = 1/400 × 4000 years
= 1 × 4000/400 years
= 4000/400 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(2) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.
(6) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 10% simple interest?
(7) If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?
(9) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.
(10) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 4% simple interest?