Question:
James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $6880
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 = $6880 – $4000 = $2880
Thus, Simple Interest = $2880
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 × 2880/4000 × 8
= 288000/32000
= 9 years (using formula)
Thus, Time (T) = 9 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 = $2880 (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 $2880, then the time = 1/320 × 2880 years
= 1 × 2880/320 years
= 2880/320 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 7 years.
(2) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?
(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
(4) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.
(5) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 7 years.
(7) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.
(8) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 3 years.
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 8 years.