Question : How much loan did Andrew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8160 to clear it?
Correct Answer $6800
Solution & Explanation
Solution
Given,
Amount (A) = $8160
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
$8160 = P (1 + 4% × 5)
⇒ $8160 = P (1 + 4/100 × 5)
⇒ $8160 = P (1 + 4 × 5/100)
⇒ $8160 = P (1 + 20/100)
⇒ $8160 = P (100 + 20/100)
⇒ $8160 = P × 120/100
⇒ P × 120/100 = $8160
⇒ P = 8160/120/100
⇒ P = 8160 × 100/120
⇒ P = 8160 × 100/120
⇒ P = 816000/120
⇒ P = $6800
Thus, the sum borrowed (P) = $6800 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 8160, then the Principal = 100/120 × 8160
= 100 × 8160/120
= 816000/120
= 6800
Thus, Principal = $6800
Thus, the sum borrowed = $6800 Answer
Similar Questions
(1) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.
(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 10% simple interest?
(7) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?