Question:
Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $7752 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7752
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 = $7752 – $5700 = $2052
Thus, Simple Interest = $2052
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 × 2052/5700 × 6
= 205200/34200
= 6 years (using formula)
Thus, Time (T) = 6 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) = 6% per annum
Simple Interest = $2052 (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 = 6% of Principal
= 6% of $5700
= 6/100 × 5700
= 6 × 5700/100
= 34200/100 = 342
Thus, simple Interest for 1 year = $342
Now,
∵ If the simple Interest is $342, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/342 years
∴ If the simple Interest is $2052, then the time = 1/342 × 2052 years
= 1 × 2052/342 years
= 2052/342 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
(3) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(4) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(6) Susan had to pay $3869 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 4 years.
(9) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?
(10) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 8% simple interest?