Question:
James took a loan of $4000 at the rate of 8% 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
6
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (R) = 8% 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 × 8
= 192000/32000
= 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) = 8% 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 = 8% of Principal
= 8% of $4000
= 8/100 × 4000
= 8 × 4000/100
= 32000/100 = 320
Thus, simple Interest for 1 year = $320
Now,
∵ If the simple Interest is $320, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/320 years
∴ If the simple Interest is $1920, then the time = 1/320 × 1920 years
= 1 × 1920/320 years
= 1920/320 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 8 years.
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 4 years.
(3) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?
(4) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(7) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 8 years.
(9) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
(10) 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.