Question:
If Donald paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4500
Solution And Explanation
Solution
Given,
Amount (A) = $5400
Rate of Simple Interest (R) = 5%
Time (T) = 4 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
$5400 = P (1 + 5% × 4)
⇒ $5400 = P (1 + 5/100 × 4)
⇒ $5400 = P (1 + 5 × 4/100)
⇒ $5400 = P (1 + 20/100)
⇒ $5400 = P (100 + 20/100)
⇒ $5400 = P × 120/100
⇒ P × 120/100 = $5400
⇒ P = 5400/120/100
⇒ P = 5400 × 100/120
⇒ P = 5400 × 100/120
⇒ P = 540000/120
⇒ P = $4500
Thus, the sum borrowed (P) = $4500 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 = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 5 = 20
Thus, simple interest for 4 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 5400, then the Principal = 100/120 × 5400
= 100 × 5400/120
= 540000/120
= 4500
Thus, Principal = $4500
Thus, the sum borrowed = $4500 Answer
Similar Questions
(1) If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.
(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 4 years.
(4) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 7 years.
(6) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.
(7) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 4% simple interest?
(8) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?
(9) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?
(10) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.