Question:
Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4200
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $6216
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 = $6216 – $4200 = $2016
Thus, Simple Interest = $2016
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 × 2016/4200 × 6
= 201600/25200
= 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) = $4200
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2016 (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 $4200
= 6/100 × 4200
= 6 × 4200/100
= 25200/100 = 252
Thus, simple Interest for 1 year = $252
Now,
∵ If the simple Interest is $252, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/252 years
∴ If the simple Interest is $2016, then the time = 1/252 × 2016 years
= 1 × 2016/252 years
= 2016/252 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) If Linda paid $3618 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 4 years.
(3) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.
(6) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?
(8) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
(9) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 4 years.