Question:
Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $8140
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are given
Formual 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 = $8140 – $5500 = $2640
Thus, Simple Interest = $2640
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 × 2640/5500 × 8
= 264000/44000
= 6 years (using formula)
Thus, Time (T) = 6 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) = $5500
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2640 (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 $5500
= 8/100 × 5500
= 8 × 5500/100
= 44000/100 = 440
Thus, simple Interest for 1 year = $440
Now,
∵ If the simple Interest is $440, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/440 years
∴ If the simple Interest is $2640, then the time = 1/440 × 2640 years
= 1 × 2640/440 years
= 2640/440 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(2) If Paul paid $5640 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(4) If Charles paid $4680 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
(6) How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?
(7) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(8) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8337.5 to clear it?
(9) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?
(10) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?