Question:
Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 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) = 10% per annum
Amount (A) = $12800
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 = $12800 – $6400 = $6400
Thus, Simple Interest = $6400
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 × 6400/6400 × 10
= 640000/64000
= 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) = 10% per annum
Simple Interest = $6400 (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 $6400, then the time = 1/640 × 6400 years
= 1 × 6400/640 years
= 6400/640 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) How much loan did Karen borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7140 to clear it?
(2) What amount does John have to pay after 6 years if he takes a loan of $3200 at 4% simple interest?
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.
(4) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(5) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
(6) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 3% simple interest?
(7) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?
(8) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.
(9) If David borrowed $3400 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) What amount does John have to pay after 5 years if he takes a loan of $3200 at 3% simple interest?