Question:
How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?
Correct Answer
$5150
Solution And Explanation
Solution
Given,
Amount (A) = $6437.5
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
$6437.5 = P (1 + 5% × 5)
⇒ $6437.5 = P (1 + 5/100 × 5)
⇒ $6437.5 = P (1 + 5 × 5/100)
⇒ $6437.5 = P (1 + 25/100)
⇒ $6437.5 = P (100 + 25/100)
⇒ $6437.5 = P × 125/100
⇒ P × 125/100 = $6437.5
⇒ P = 6437.5/125/100
⇒ P = 6437.5 × 100/125
⇒ P = 6437.5 × 100/125
⇒ P = 643750/125
⇒ P = $5150
Thus, the sum borrowed (P) = $5150 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 6437.5, then the Principal = 100/125 × 6437.5
= 100 × 6437.5/125
= 643750/125
= 5150
Thus, Principal = $5150
Thus, the sum borrowed = $5150 Answer
Similar Questions
(1) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9360 to clear it?
(2) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 3 years.
(4) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 7% simple interest?
(5) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 4 years.
(7) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?
(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.
(9) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?
(10) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 8% simple interest?