Question : Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
Correct Answer 10
Solution & Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $11400
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 = $11400 – $5700 = $5700
Thus, Simple Interest = $5700
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 × 5700/5700 × 10
= 570000/57000
= 10 years (using formula)
Thus, Time (T) = 10 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) = 10% per annum
Simple Interest = $5700 (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 $5700
= 10/100 × 5700
= 10 × 5700/100
= 57000/100 = 570
Thus, simple Interest for 1 year = $570
Now,
∵ If the simple Interest is $570, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/570 years
∴ If the simple Interest is $5700, then the time = 1/570 × 5700 years
= 1 × 5700/570 years
= 5700/570 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) In how much time a principal of $3150 will amount to $3339 at a simple interest of 2% per annum?
(2) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 3% simple interest?
(3) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?
(4) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.
(5) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 4 years.
(6) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.
(7) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 8 years.
(9) In how much time a principal of $3150 will amount to $3276 at a simple interest of 2% per annum?
(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 4 years.