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 Patricia have to pay after 5 years if he takes a loan of $3150 at 2% simple interest?
(2) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.
(3) How much loan did Richard borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7000 to clear it?
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.
(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(6) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 8 years.
(8) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 3 years.
(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.
(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 7 years.