Question:
How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?
Correct Answer
$5300
Solution And Explanation
Solution
Given,
Amount (A) = $6360
Rate of Simple Interest (R) = 4%
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
$6360 = P (1 + 4% × 5)
⇒ $6360 = P (1 + 4/100 × 5)
⇒ $6360 = P (1 + 4 × 5/100)
⇒ $6360 = P (1 + 20/100)
⇒ $6360 = P (100 + 20/100)
⇒ $6360 = P × 120/100
⇒ P × 120/100 = $6360
⇒ P = 6360/120/100
⇒ P = 6360 × 100/120
⇒ P = 6360 × 100/120
⇒ P = 636000/120
⇒ P = $5300
Thus, the sum borrowed (P) = $5300 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 6360, then the Principal = 100/120 × 6360
= 100 × 6360/120
= 636000/120
= 5300
Thus, Principal = $5300
Thus, the sum borrowed = $5300 Answer
Similar Questions
(1) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?
(2) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.
(3) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(4) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?
(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 7 years.
(6) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?
(7) If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.
(9) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?
(10) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.