Question:
Joseph took a loan of $5400 at the rate of 8% 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
7
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (R) = 8% 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 × 8
= 302400/43200
= 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) = 8% 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 = 8% of Principal
= 8% of $5400
= 8/100 × 5400
= 8 × 5400/100
= 43200/100 = 432
Thus, simple Interest for 1 year = $432
Now,
∵ If the simple Interest is $432, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/432 years
∴ If the simple Interest is $3024, then the time = 1/432 × 3024 years
= 1 × 3024/432 years
= 3024/432 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.
(2) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?
(3) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
(4) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6258 to clear the loan, then find the time period of the loan.
(5) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?
(6) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?
(7) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 3 years.
(9) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(10) If John paid $3584 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.