Question:
How much loan did Anthony borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7875 to clear it?
Correct Answer
$6300
Solution And Explanation
Solution
Given,
Amount (A) = $7875
Rate of Simple Interest (R) = 5%
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
$7875 = P (1 + 5% × 5)
⇒ $7875 = P (1 + 5/100 × 5)
⇒ $7875 = P (1 + 5 × 5/100)
⇒ $7875 = P (1 + 25/100)
⇒ $7875 = P (100 + 25/100)
⇒ $7875 = P × 125/100
⇒ P × 125/100 = $7875
⇒ P = 7875/125/100
⇒ P = 7875 × 100/125
⇒ P = 7875 × 100/125
⇒ P = 787500/125
⇒ P = $6300
Thus, the sum borrowed (P) = $6300 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 7875, then the Principal = 100/125 × 7875
= 100 × 7875/125
= 787500/125
= 6300
Thus, Principal = $6300
Thus, the sum borrowed = $6300 Answer
Similar Questions
(1) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 2% simple interest?
(2) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(5) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 5% simple interest?
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 3 years.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.
(8) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.
(10) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.