Question:
How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?
Correct Answer
$7850
Solution And Explanation
Solution
Given,
Amount (A) = $9420
Rate of Simple Interest (R) = 4%
Time (T) = 5 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
$9420 = P (1 + 4% × 5)
⇒ $9420 = P (1 + 4/100 × 5)
⇒ $9420 = P (1 + 4 × 5/100)
⇒ $9420 = P (1 + 20/100)
⇒ $9420 = P (100 + 20/100)
⇒ $9420 = P × 120/100
⇒ P × 120/100 = $9420
⇒ P = 9420/120/100
⇒ P = 9420 × 100/120
⇒ P = 9420 × 100/120
⇒ P = 942000/120
⇒ P = $7850
Thus, the sum borrowed (P) = $7850 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 = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 9420, then the Principal = 100/120 × 9420
= 100 × 9420/120
= 942000/120
= 7850
Thus, Principal = $7850
Thus, the sum borrowed = $7850 Answer
Similar Questions
(1) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?
(2) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.
(4) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(5) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 4% simple interest?
(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?
(8) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 8 years.
(10) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 10% simple interest?