Question:
Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4700
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7238
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 = $7238 – $4700 = $2538
Thus, Simple Interest = $2538
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 × 2538/4700 × 6
= 253800/28200
= 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) = $4700
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2538 (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 $4700
= 6/100 × 4700
= 6 × 4700/100
= 28200/100 = 282
Thus, simple Interest for 1 year = $282
Now,
∵ If the simple Interest is $282, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/282 years
∴ If the simple Interest is $2538, then the time = 1/282 × 2538 years
= 1 × 2538/282 years
= 2538/282 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(2) If Kenneth paid $5600 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 3 years.
(4) How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?
(5) Elizabeth had to pay $3864 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 9% simple interest?
(7) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(8) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 7 years.
(9) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.
(10) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6392 to clear the loan, then find the time period of the loan.