Question:
Robert took a loan of $4200 at the rate of 6% 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
7
Solution And Explanation
Solution
Given,
Principal (P) = $4200
Rate of Simple Interest (R) = 6% 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 × 6
= 176400/25200
= 7 years (using formula)
Thus, Time (T) = 7 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 = $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 = 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 $1764, then the time = 1/252 × 1764 years
= 1 × 1764/252 years
= 1764/252 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 3 years.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.
(3) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.
(4) If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.
(6) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.
(7) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(9) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?