Question:
James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $6400
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 = $6400 – $4000 = $2400
Thus, Simple Interest = $2400
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 × 2400/4000 × 10
= 240000/40000
= 6 years (using formula)
Thus, Time (T) = 6 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 = $2400 (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 $2400, then the time = 1/400 × 2400 years
= 1 × 2400/400 years
= 2400/400 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?
(2) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 10% simple interest?
(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.
(6) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.
(8) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.
(10) Karen had to pay $4305.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.