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) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
(3) How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?
(4) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?
(6) How much loan did Richard borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7000 to clear it?
(7) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?
(8) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(9) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.