Question:
Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10070
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 = $10070 – $5300 = $4770
Thus, Simple Interest = $4770
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 × 4770/5300 × 9
= 477000/47700
= 10 years (using formula)
Thus, Time (T) = 10 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) = $5300
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4770 (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 = 9% of Principal
= 9% of $5300
= 9/100 × 5300
= 9 × 5300/100
= 47700/100 = 477
Thus, simple Interest for 1 year = $477
Now,
∵ If the simple Interest is $477, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/477 years
∴ If the simple Interest is $4770, then the time = 1/477 × 4770 years
= 1 × 4770/477 years
= 4770/477 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.
(2) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(3) If Jessica paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.
(5) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.
(6) How much loan did Karen borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7140 to clear it?
(7) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(8) In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?
(9) What amount will be due after 2 years if James borrowed a sum of $3000 at a 5% simple interest?
(10) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?