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) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(2) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(3) How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?
(4) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.
(6) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 8% simple interest?
(7) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(8) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(9) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?
(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.