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) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 3 years.
(3) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(4) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.
(5) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(6) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6258 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.
(10) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.