Question:
Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6400
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $10880
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 = $10880 – $6400 = $4480
Thus, Simple Interest = $4480
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 × 4480/6400 × 10
= 448000/64000
= 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) = $6400
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4480 (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 $4480, then the time = 1/640 × 4480 years
= 1 × 4480/640 years
= 4480/640 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.
(2) Paul had to pay $5405 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 8 years.
(4) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(5) How much loan did Brian borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9000 to clear it?
(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?
(7) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?
(8) Robert had to pay $3379 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 9% simple interest?
(10) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.