Question:
How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?
Correct Answer
$6250
Solution And Explanation
Solution
Given,
Amount (A) = $7500
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
$7500 = P (1 + 4% × 5)
⇒ $7500 = P (1 + 4/100 × 5)
⇒ $7500 = P (1 + 4 × 5/100)
⇒ $7500 = P (1 + 20/100)
⇒ $7500 = P (100 + 20/100)
⇒ $7500 = P × 120/100
⇒ P × 120/100 = $7500
⇒ P = 7500/120/100
⇒ P = 7500 × 100/120
⇒ P = 7500 × 100/120
⇒ P = 750000/120
⇒ P = $6250
Thus, the sum borrowed (P) = $6250 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 7500, then the Principal = 100/120 × 7500
= 100 × 7500/120
= 750000/120
= 6250
Thus, Principal = $6250
Thus, the sum borrowed = $6250 Answer
Similar Questions
(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 7 years.
(2) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?
(3) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.
(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.
(7) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 7 years.
(9) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.
(10) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.