Question:
How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?
Correct Answer
$5100
Solution And Explanation
Solution
Given,
Amount (A) = $5610
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
$5610 = P (1 + 2% × 5)
⇒ $5610 = P (1 + 2/100 × 5)
⇒ $5610 = P (1 + 2 × 5/100)
⇒ $5610 = P (1 + 10/100)
⇒ $5610 = P (100 + 10/100)
⇒ $5610 = P × 110/100
⇒ P × 110/100 = $5610
⇒ P = 5610/110/100
⇒ P = 5610 × 100/110
⇒ P = 5610 × 100/110
⇒ P = 561000/110
⇒ P = $5100
Thus, the sum borrowed (P) = $5100 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 5610, then the Principal = 100/110 × 5610
= 100 × 5610/110
= 561000/110
= 5100
Thus, Principal = $5100
Thus, the sum borrowed = $5100 Answer
Similar Questions
(1) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 3 years.
(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 4 years.
(5) What amount will be due after 2 years if William borrowed a sum of $3250 at a 5% simple interest?
(6) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
(7) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?
(9) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?
(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 4% simple interest?