Question:
Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4200
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $5964
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 = $5964 – $4200 = $1764
Thus, Simple Interest = $1764
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 × 1764/4200 × 7
= 176400/29400
= 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) = $4200
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $1764 (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 = 7% of Principal
= 7% of $4200
= 7/100 × 4200
= 7 × 4200/100
= 29400/100 = 294
Thus, simple Interest for 1 year = $294
Now,
∵ If the simple Interest is $294, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/294 years
∴ If the simple Interest is $1764, then the time = 1/294 × 1764 years
= 1 × 1764/294 years
= 1764/294 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(2) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(3) If Lisa paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8024 to clear the loan, then find the time period of the loan.
(5) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 4 years.
(7) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?
(8) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?
(9) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?
(10) If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.