Question:
If Elizabeth paid $3726 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3450
Solution And Explanation
Solution
Given,
Amount (A) = $3726
Rate of Simple Interest (R) = 2%
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
$3726 = P (1 + 2% × 4)
⇒ $3726 = P (1 + 2/100 × 4)
⇒ $3726 = P (1 + 2 × 4/100)
⇒ $3726 = P (1 + 8/100)
⇒ $3726 = P (100 + 8/100)
⇒ $3726 = P × 108/100
⇒ P × 108/100 = $3726
⇒ P = 3726/108/100
⇒ P = 3726 × 100/108
⇒ P = 3726 × 100/108
⇒ P = 372600/108
⇒ 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 3726, then the Principal = 100/108 × 3726
= 100 × 3726/108
= 372600/108
= 3450
Thus, Principal = $3450
Thus, the sum borrowed = $3450 Answer
Similar Questions
(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 6% simple interest?
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.
(3) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.
(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?
(5) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 8% simple interest?
(6) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?
(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?
(9) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(10) Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.