Question:
Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4300
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7052
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 = $7052 – $4300 = $2752
Thus, Simple Interest = $2752
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 × 2752/4300 × 8
= 275200/34400
= 8 years (using formula)
Thus, Time (T) = 8 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) = $4300
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2752 (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 = 8% of Principal
= 8% of $4300
= 8/100 × 4300
= 8 × 4300/100
= 34400/100 = 344
Thus, simple Interest for 1 year = $344
Now,
∵ If the simple Interest is $344, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/344 years
∴ If the simple Interest is $2752, then the time = 1/344 × 2752 years
= 1 × 2752/344 years
= 2752/344 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?
(2) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.
(4) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(5) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.
(7) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.
(8) If Linda paid $3752 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 7 years.
(10) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.