Question:
Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6300
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $11340
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 = $11340 – $6300 = $5040
Thus, Simple Interest = $5040
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 × 5040/6300 × 10
= 504000/63000
= 8 years (using formula)
Thus, Time (T) = 8 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) = $6300
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $5040 (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 $6300
= 10/100 × 6300
= 10 × 6300/100
= 63000/100 = 630
Thus, simple Interest for 1 year = $630
Now,
∵ If the simple Interest is $630, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/630 years
∴ If the simple Interest is $5040, then the time = 1/630 × 5040 years
= 1 × 5040/630 years
= 5040/630 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 3 years.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.
(4) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.
(6) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 9% simple interest?
(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 4 years.
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.
(10) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.