Question:
If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4450
Solution And Explanation
Solution
Given,
Amount (A) = $5340
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
$5340 = P (1 + 5% × 4)
⇒ $5340 = P (1 + 5/100 × 4)
⇒ $5340 = P (1 + 5 × 4/100)
⇒ $5340 = P (1 + 20/100)
⇒ $5340 = P (100 + 20/100)
⇒ $5340 = P × 120/100
⇒ P × 120/100 = $5340
⇒ P = 5340/120/100
⇒ P = 5340 × 100/120
⇒ P = 5340 × 100/120
⇒ P = 534000/120
⇒ P = $4450
Thus, the sum borrowed (P) = $4450 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 5340, then the Principal = 100/120 × 5340
= 100 × 5340/120
= 534000/120
= 4450
Thus, Principal = $4450
Thus, the sum borrowed = $4450 Answer
Similar Questions
(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 8 years.
(2) What amount does James have to pay after 5 years if he takes a loan of $3000 at 10% simple interest?
(3) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.
(4) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 6% simple interest?
(5) In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?
(6) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 7% simple interest?
(7) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 8% simple interest?
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 7 years.
(9) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.