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) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?
(2) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.
(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?
(4) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 7 years.
(6) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?
(8) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 6% simple interest?
(9) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 8% simple interest?
(10) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.