Question:
How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?
Correct Answer
$6500
Solution And Explanation
Solution
Given,
Amount (A) = $7800
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
$7800 = P (1 + 4% × 5)
⇒ $7800 = P (1 + 4/100 × 5)
⇒ $7800 = P (1 + 4 × 5/100)
⇒ $7800 = P (1 + 20/100)
⇒ $7800 = P (100 + 20/100)
⇒ $7800 = P × 120/100
⇒ P × 120/100 = $7800
⇒ P = 7800/120/100
⇒ P = 7800 × 100/120
⇒ P = 7800 × 100/120
⇒ P = 780000/120
⇒ P = $6500
Thus, the sum borrowed (P) = $6500 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 7800, then the Principal = 100/120 × 7800
= 100 × 7800/120
= 780000/120
= 6500
Thus, Principal = $6500
Thus, the sum borrowed = $6500 Answer
Similar Questions
(1) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.
(3) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 7 years.
(5) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.
(7) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.
(8) If Emily paid $5130 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 7 years.
(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.