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 And 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) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?
(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.
(3) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.
(5) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.
(6) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
(7) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.
(9) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 4 years.
(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 8 years.