Question:
James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $6800
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 = $6800 – $4000 = $2800
Thus, Simple Interest = $2800
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 × 2800/4000 × 10
= 280000/40000
= 7 years (using formula)
Thus, Time (T) = 7 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) = $4000
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $2800 (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 $4000
= 10/100 × 4000
= 10 × 4000/100
= 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 $2800, then the time = 1/400 × 2800 years
= 1 × 2800/400 years
= 2800/400 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?
(2) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.
(5) How much loan did Nancy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6765 to clear it?
(6) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
(7) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.
(9) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
(10) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.