Question:
Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4300
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7396
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 = $7396 – $4300 = $3096
Thus, Simple Interest = $3096
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 × 3096/4300 × 8
= 309600/34400
= 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) = $4300
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3096 (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 $3096, then the time = 1/344 × 3096 years
= 1 × 3096/344 years
= 3096/344 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 7 years.
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.
(3) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(4) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.
(6) If William paid $4060 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 to clear the loan, then find the time period of the loan.
(8) How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?
(9) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.