Question:
How much loan did Amanda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8580 to clear it?
Correct Answer
$7150
Solution And Explanation
Solution
Given,
Amount (A) = $8580
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
$8580 = P (1 + 4% × 5)
⇒ $8580 = P (1 + 4/100 × 5)
⇒ $8580 = P (1 + 4 × 5/100)
⇒ $8580 = P (1 + 20/100)
⇒ $8580 = P (100 + 20/100)
⇒ $8580 = P × 120/100
⇒ P × 120/100 = $8580
⇒ P = 8580/120/100
⇒ P = 8580 × 100/120
⇒ P = 8580 × 100/120
⇒ P = 858000/120
⇒ P = $7150
Thus, the sum borrowed (P) = $7150 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 8580, then the Principal = 100/120 × 8580
= 100 × 8580/120
= 858000/120
= 7150
Thus, Principal = $7150
Thus, the sum borrowed = $7150 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9685 to clear the loan, then find the time period of the loan.
(2) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.
(4) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.
(6) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.
(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.
(10) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.