Question:
Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6400
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $12160
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 = $12160 – $6400 = $5760
Thus, Simple Interest = $5760
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 × 5760/6400 × 9
= 576000/57600
= 10 years (using formula)
Thus, Time (T) = 10 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) = $6400
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $5760 (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 = 9% of Principal
= 9% of $6400
= 9/100 × 6400
= 9 × 6400/100
= 57600/100 = 576
Thus, simple Interest for 1 year = $576
Now,
∵ If the simple Interest is $576, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/576 years
∴ If the simple Interest is $5760, then the time = 1/576 × 5760 years
= 1 × 5760/576 years
= 5760/576 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(2) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(3) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 7 years.
(5) If Joseph paid $4144 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.
(7) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 8% simple interest?
(8) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?
(9) If Jessica paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.