Question:
If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4450
Solution And Explanation
Solution
Given,
Amount (A) = $5162
Rate of Simple Interest (R) = 4%
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
$5162 = P (1 + 4% × 4)
⇒ $5162 = P (1 + 4/100 × 4)
⇒ $5162 = P (1 + 4 × 4/100)
⇒ $5162 = P (1 + 16/100)
⇒ $5162 = P (100 + 16/100)
⇒ $5162 = P × 116/100
⇒ P × 116/100 = $5162
⇒ P = 5162/116/100
⇒ P = 5162 × 100/116
⇒ P = 5162 × 100/116
⇒ P = 516200/116
⇒ 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 = 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 = 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 × 4 = 16
Thus, simple interest for 4 years = 16
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 16 = 116
Calculation of the Principal
Now,
∵ If the Amount is 116, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/116
∴ If the Amount is 5162, then the Principal = 100/116 × 5162
= 100 × 5162/116
= 516200/116
= 4450
Thus, Principal = $4450
Thus, the sum borrowed = $4450 Answer
Similar Questions
(1) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.
(2) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.
(3) How much loan did Patricia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6180 to clear it?
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.
(5) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 7% simple interest?
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 8 years.
(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?
(8) If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.