Question:
Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9536 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) = 7% per annum
Amount (A) = $9536
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 = $9536 – $6400 = $3136
Thus, Simple Interest = $3136
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 × 3136/6400 × 7
= 313600/44800
= 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) = 7% per annum
Simple Interest = $3136 (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 = 7% of Principal
= 7% of $6400
= 7/100 × 6400
= 7 × 6400/100
= 44800/100 = 448
Thus, simple Interest for 1 year = $448
Now,
∵ If the simple Interest is $448, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/448 years
∴ If the simple Interest is $3136, then the time = 1/448 × 3136 years
= 1 × 3136/448 years
= 3136/448 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(2) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.
(4) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(5) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
(6) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) If Robert paid $3348 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 4 years.
(10) If Kimberly paid $5022 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.