Question : How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
Correct Answer $5600
Solution & Explanation
Solution
Given,
Amount (A) = $6720
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
$6720 = P (1 + 4% × 5)
⇒ $6720 = P (1 + 4/100 × 5)
⇒ $6720 = P (1 + 4 × 5/100)
⇒ $6720 = P (1 + 20/100)
⇒ $6720 = P (100 + 20/100)
⇒ $6720 = P × 120/100
⇒ P × 120/100 = $6720
⇒ P = 6720/120/100
⇒ P = 6720 × 100/120
⇒ P = 6720 × 100/120
⇒ P = 672000/120
⇒ P = $5600
Thus, the sum borrowed (P) = $5600 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 6720, then the Principal = 100/120 × 6720
= 100 × 6720/120
= 672000/120
= 5600
Thus, Principal = $5600
Thus, the sum borrowed = $5600 Answer
Similar Questions
(2) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?
(4) What amount does David have to pay after 5 years if he takes a loan of $3400 at 2% simple interest?
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.
(9) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.