Question:
How much loan did Patricia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6180 to clear it?
Correct Answer
$5150
Solution And Explanation
Solution
Given,
Amount (A) = $6180
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
$6180 = P (1 + 4% × 5)
⇒ $6180 = P (1 + 4/100 × 5)
⇒ $6180 = P (1 + 4 × 5/100)
⇒ $6180 = P (1 + 20/100)
⇒ $6180 = P (100 + 20/100)
⇒ $6180 = P × 120/100
⇒ P × 120/100 = $6180
⇒ P = 6180/120/100
⇒ P = 6180 × 100/120
⇒ P = 6180 × 100/120
⇒ P = 618000/120
⇒ P = $5150
Thus, the sum borrowed (P) = $5150 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 6180, then the Principal = 100/120 × 6180
= 100 × 6180/120
= 618000/120
= 5150
Thus, Principal = $5150
Thus, the sum borrowed = $5150 Answer
Similar Questions
(1) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 10% simple interest?
(2) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10780 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 8% simple interest?
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 8 years.
(5) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 7 years.
(7) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?
(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.
(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 4 years.
(10) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.