Question:
Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6392 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4700
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $6392
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 = $6392 – $4700 = $1692
Thus, Simple Interest = $1692
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 × 1692/4700 × 6
= 169200/28200
= 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) = $4700
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $1692 (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 $4700
= 6/100 × 4700
= 6 × 4700/100
= 28200/100 = 282
Thus, simple Interest for 1 year = $282
Now,
∵ If the simple Interest is $282, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/282 years
∴ If the simple Interest is $1692, then the time = 1/282 × 1692 years
= 1 × 1692/282 years
= 1692/282 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 3 years.
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 3 years.
(4) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(5) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?
(6) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?
(8) What amount does James have to pay after 6 years if he takes a loan of $3000 at 3% simple interest?
(9) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.