Question : How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?
Correct Answer $6700
Solution & Explanation
Solution
Given,
Amount (A) = $8040
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
$8040 = P (1 + 4% × 5)
⇒ $8040 = P (1 + 4/100 × 5)
⇒ $8040 = P (1 + 4 × 5/100)
⇒ $8040 = P (1 + 20/100)
⇒ $8040 = P (100 + 20/100)
⇒ $8040 = P × 120/100
⇒ P × 120/100 = $8040
⇒ P = 8040/120/100
⇒ P = 8040 × 100/120
⇒ P = 8040 × 100/120
⇒ P = 804000/120
⇒ P = $6700
Thus, the sum borrowed (P) = $6700 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 8040, then the Principal = 100/120 × 8040
= 100 × 8040/120
= 804000/120
= 6700
Thus, Principal = $6700
Thus, the sum borrowed = $6700 Answer
Similar Questions
(1) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?
(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.
(3) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.
(5) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 7% simple interest?
(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.
(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 6% simple interest?
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.