Question:
How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?
Correct Answer
$6750
Solution And Explanation
Solution
Given,
Amount (A) = $8100
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
$8100 = P (1 + 4% × 5)
⇒ $8100 = P (1 + 4/100 × 5)
⇒ $8100 = P (1 + 4 × 5/100)
⇒ $8100 = P (1 + 20/100)
⇒ $8100 = P (100 + 20/100)
⇒ $8100 = P × 120/100
⇒ P × 120/100 = $8100
⇒ P = 8100/120/100
⇒ P = 8100 × 100/120
⇒ P = 8100 × 100/120
⇒ P = 810000/120
⇒ P = $6750
Thus, the sum borrowed (P) = $6750 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 8100, then the Principal = 100/120 × 8100
= 100 × 8100/120
= 810000/120
= 6750
Thus, Principal = $6750
Thus, the sum borrowed = $6750 Answer
Similar Questions
(1) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.
(3) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 4 years.
(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.
(6) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.
(7) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 8 years.