Question:
William took a loan of $5000 at the rate of 10% 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
8
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (R) = 10% 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 × 10
= 400000/50000
= 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) = $5000
Rate of Simple Interest (R) = 10% 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 = 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 $4000, then the time = 1/500 × 4000 years
= 1 × 4000/500 years
= 4000/500 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.
(2) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.
(3) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?
(4) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.
(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(7) If Lisa paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
(9) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 5% simple interest?
(10) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.