Question:
Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6400
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $11520
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are given
Formual 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 = $11520 – $6400 = $5120
Thus, Simple Interest = $5120
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 × 5120/6400 × 10
= 512000/64000
= 8 years (using formula)
Thus, Time (T) = 8 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 = $5120 (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 $5120, then the time = 1/640 × 5120 years
= 1 × 5120/640 years
= 5120/640 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(2) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(3) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 3 years.
(5) James had to pay $3360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.
(8) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.
(10) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.