Question:
If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3550
Solution And Explanation
Solution
Given,
Amount (A) = $4260
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
$4260 = P (1 + 5% × 4)
⇒ $4260 = P (1 + 5/100 × 4)
⇒ $4260 = P (1 + 5 × 4/100)
⇒ $4260 = P (1 + 20/100)
⇒ $4260 = P (100 + 20/100)
⇒ $4260 = P × 120/100
⇒ P × 120/100 = $4260
⇒ P = 4260/120/100
⇒ P = 4260 × 100/120
⇒ P = 4260 × 100/120
⇒ P = 426000/120
⇒ P = $3550
Thus, the sum borrowed (P) = $3550 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 4260, then the Principal = 100/120 × 4260
= 100 × 4260/120
= 426000/120
= 3550
Thus, Principal = $3550
Thus, the sum borrowed = $3550 Answer
Similar Questions
(1) What amount does John have to pay after 5 years if he takes a loan of $3200 at 10% simple interest?
(2) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?
(3) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(6) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.
(7) How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?
(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.
(9) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(10) How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?