Question:
James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $5920
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 = $5920 – $4000 = $1920
Thus, Simple Interest = $1920
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 × 1920/4000 × 6
= 192000/24000
= 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) = $4000
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $1920 (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 = 6% of Principal
= 6% of $4000
= 6/100 × 4000
= 6 × 4000/100
= 24000/100 = 240
Thus, simple Interest for 1 year = $240
Now,
∵ If the simple Interest is $240, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/240 years
∴ If the simple Interest is $1920, then the time = 1/240 × 1920 years
= 1 × 1920/240 years
= 1920/240 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(2) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 4 years.
(3) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 7% simple interest?
(4) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 3 years.
(6) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.
(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 4 years.
(10) How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?