Question:
Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $8424
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 = $8424 – $5400 = $3024
Thus, Simple Interest = $3024
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 × 3024/5400 × 7
= 302400/37800
= 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) = $5400
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3024 (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 $3024, then the time = 1/378 × 3024 years
= 1 × 3024/378 years
= 3024/378 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.
(2) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?
(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?
(4) If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 7 years.
(6) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 7% simple interest?
(7) How much loan did Brian borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9000 to clear it?
(8) In how much time a principal of $3150 will amount to $3402 at a simple interest of 2% per annum?
(9) What amount will be due after 2 years if James borrowed a sum of $3000 at a 10% simple interest?
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.