Question:
Matthew took a loan of $6400 at the rate of 10% 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
9
Solution And Explanation
Solution
Given,
Principal (P) = $6400
Rate of Simple Interest (R) = 10% 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 × 10
= 576000/64000
= 9 years (using formula)
Thus, Time (T) = 9 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) = 10% 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 = 10% of Principal
= 10% of $6400
= 10/100 × 6400
= 10 × 6400/100
= 64000/100 = 640
Thus, simple Interest for 1 year = $640
Now,
∵ If the simple Interest is $640, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/640 years
∴ If the simple Interest is $5760, then the time = 1/640 × 5760 years
= 1 × 5760/640 years
= 5760/640 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) How much loan did Steven borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8250 to clear it?
(2) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?
(3) If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 3 years.
(5) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 8% simple interest?
(6) How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?
(7) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?
(8) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.
(10) If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.