Question:
How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?
Correct Answer
$6350
Solution And Explanation
Solution
Given,
Amount (A) = $6985
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
$6985 = P (1 + 2% × 5)
⇒ $6985 = P (1 + 2/100 × 5)
⇒ $6985 = P (1 + 2 × 5/100)
⇒ $6985 = P (1 + 10/100)
⇒ $6985 = P (100 + 10/100)
⇒ $6985 = P × 110/100
⇒ P × 110/100 = $6985
⇒ P = 6985/110/100
⇒ P = 6985 × 100/110
⇒ P = 6985 × 100/110
⇒ P = 698500/110
⇒ P = $6350
Thus, the sum borrowed (P) = $6350 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 6985, then the Principal = 100/110 × 6985
= 100 × 6985/110
= 698500/110
= 6350
Thus, Principal = $6350
Thus, the sum borrowed = $6350 Answer
Similar Questions
(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.
(2) If Kenneth paid $5600 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 9% simple interest?
(4) How much loan did Paul borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8375 to clear it?
(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 10% simple interest?
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.
(7) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.
(9) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 3 years.