Question:
Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4100
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $6109
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 = $6109 – $4100 = $2009
Thus, Simple Interest = $2009
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 × 2009/4100 × 7
= 200900/28700
= 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) = $4100
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2009 (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 $4100
= 7/100 × 4100
= 7 × 4100/100
= 28700/100 = 287
Thus, simple Interest for 1 year = $287
Now,
∵ If the simple Interest is $287, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/287 years
∴ If the simple Interest is $2009, then the time = 1/287 × 2009 years
= 1 × 2009/287 years
= 2009/287 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 7 years.
(2) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 7 years.
(3) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 8 years.
(5) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.
(7) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11946 to clear the loan, then find the time period of the loan.
(8) If Robert borrowed $3100 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(9) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.