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) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.
(2) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) If Elizabeth paid $3864 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(5) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.
(9) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(10) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.