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) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?
(2) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 7 years.
(4) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 3 years.
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 4 years.
(7) How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?
(8) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.
(10) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?