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) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 8 years.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.
(3) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 2% simple interest?
(4) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 3 years.
(6) Steven had to pay $5014 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 4 years.
(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 7 years.
(9) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.