Question:
If Elizabeth paid $3864 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3450
Solution And Explanation
Solution
Given,
Amount (A) = $3864
Rate of Simple Interest (R) = 3%
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
$3864 = P (1 + 3% × 4)
⇒ $3864 = P (1 + 3/100 × 4)
⇒ $3864 = P (1 + 3 × 4/100)
⇒ $3864 = P (1 + 12/100)
⇒ $3864 = P (100 + 12/100)
⇒ $3864 = P × 112/100
⇒ P × 112/100 = $3864
⇒ P = 3864/112/100
⇒ P = 3864 × 100/112
⇒ P = 3864 × 100/112
⇒ P = 386400/112
⇒ P = $3450
Thus, the sum borrowed (P) = $3450 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 3864, then the Principal = 100/112 × 3864
= 100 × 3864/112
= 386400/112
= 3450
Thus, Principal = $3450
Thus, the sum borrowed = $3450 Answer
Similar Questions
(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 7 years.
(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 3 years.
(3) Andrew had to pay $5232 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
(5) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 5% simple interest?
(6) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?
(7) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5712 to clear the loan, then find the time period of the loan.
(8) How much loan did Susan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6780 to clear it?
(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?
(10) How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?