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) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(2) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?
(4) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
(5) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(6) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10860 to clear the loan, then find the time period of the loan.
(7) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 8 years.
(10) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.