Question:
How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?
Correct Answer
$5350
Solution And Explanation
Solution
Given,
Amount (A) = $5885
Rate of Simple Interest (R) = 2%
Time (T) = 5 years
Thus, Principal (P) = ?
Method (1) Using Formula
Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given
Formula to find the Principal (P)
Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)
⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]
⇒ A = P (1 + RT)
Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given
In the given question, we need to find the Principal (P)
Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get
$5885 = P (1 + 2% × 5)
⇒ $5885 = P (1 + 2/100 × 5)
⇒ $5885 = P (1 + 2 × 5/100)
⇒ $5885 = P (1 + 10/100)
⇒ $5885 = P (100 + 10/100)
⇒ $5885 = P × 110/100
⇒ P × 110/100 = $5885
⇒ P = 5885/110/100
⇒ P = 5885 × 100/110
⇒ P = 5885 × 100/110
⇒ P = 588500/110
⇒ P = $5350
Thus, the sum borrowed (P) = $5350 Answer
Method (1) Using Unitary Method
Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given
Calculation of the Simple Interest
Let, the principal = 100
Here, since rate of simple interest = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
Calculation of the Amount
Since, in the question, time = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 5885, then the Principal = 100/110 × 5885
= 100 × 5885/110
= 588500/110
= 5350
Thus, Principal = $5350
Thus, the sum borrowed = $5350 Answer
Similar Questions
(1) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.
(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.
(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.
(6) How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 3 years.
(8) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?
(10) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?