Question:
How much loan did Steven borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8250 to clear it?
Correct Answer
$6600
Solution And Explanation
Solution
Given,
Amount (A) = $8250
Rate of Simple Interest (R) = 5%
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
$8250 = P (1 + 5% × 5)
⇒ $8250 = P (1 + 5/100 × 5)
⇒ $8250 = P (1 + 5 × 5/100)
⇒ $8250 = P (1 + 25/100)
⇒ $8250 = P (100 + 25/100)
⇒ $8250 = P × 125/100
⇒ P × 125/100 = $8250
⇒ P = 8250/125/100
⇒ P = 8250 × 100/125
⇒ P = 8250 × 100/125
⇒ P = 825000/125
⇒ P = $6600
Thus, the sum borrowed (P) = $6600 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 8250, then the Principal = 100/125 × 8250
= 100 × 8250/125
= 825000/125
= 6600
Thus, Principal = $6600
Thus, the sum borrowed = $6600 Answer
Similar Questions
(1) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 7% simple interest?
(2) If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 4 years.
(4) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?
(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 8 years.
(6) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(7) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(8) If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(10) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?