Question:
Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $8046
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 = $8046 – $5400 = $2646
Thus, Simple Interest = $2646
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 × 2646/5400 × 7
= 264600/37800
= 7 years (using formula)
Thus, Time (T) = 7 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) = $5400
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2646 (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 = 7% of Principal
= 7% of $5400
= 7/100 × 5400
= 7 × 5400/100
= 37800/100 = 378
Thus, simple Interest for 1 year = $378
Now,
∵ If the simple Interest is $378, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/378 years
∴ If the simple Interest is $2646, then the time = 1/378 × 2646 years
= 1 × 2646/378 years
= 2646/378 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?
(3) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5712 to clear the loan, then find the time period of the loan.
(4) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.
(6) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.
(7) If Patricia paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 4 years.
(9) If Margaret paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.