Question:
Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $8493
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 = $8493 – $5700 = $2793
Thus, Simple Interest = $2793
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 × 2793/5700 × 7
= 279300/39900
= 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) = $5700
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2793 (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 $5700
= 7/100 × 5700
= 7 × 5700/100
= 39900/100 = 399
Thus, simple Interest for 1 year = $399
Now,
∵ If the simple Interest is $399, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/399 years
∴ If the simple Interest is $2793, then the time = 1/399 × 2793 years
= 1 × 2793/399 years
= 2793/399 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(2) If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?
(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.
(5) Richard had to pay $3924 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 3 years.
(7) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 4% simple interest?
(8) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 4 years.
(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.