Question:
If Elizabeth paid $4002 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3450
Solution And Explanation
Solution
Given,
Amount (A) = $4002
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
$4002 = P (1 + 4% × 4)
⇒ $4002 = P (1 + 4/100 × 4)
⇒ $4002 = P (1 + 4 × 4/100)
⇒ $4002 = P (1 + 16/100)
⇒ $4002 = P (100 + 16/100)
⇒ $4002 = P × 116/100
⇒ P × 116/100 = $4002
⇒ P = 4002/116/100
⇒ P = 4002 × 100/116
⇒ P = 4002 × 100/116
⇒ P = 400200/116
⇒ 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 = 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 4002, then the Principal = 100/116 × 4002
= 100 × 4002/116
= 400200/116
= 3450
Thus, Principal = $3450
Thus, the sum borrowed = $3450 Answer
Similar Questions
(1) If Robert borrowed $3100 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(2) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?
(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 9% simple interest?
(4) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(5) What amount does William have to pay after 5 years if he takes a loan of $3500 at 7% simple interest?
(6) Kimberly had to pay $5347.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
(8) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(9) If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.