Question:
How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?
Correct Answer
$6800
Solution And Explanation
Solution
Given,
Amount (A) = $8500
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
$8500 = P (1 + 5% × 5)
⇒ $8500 = P (1 + 5/100 × 5)
⇒ $8500 = P (1 + 5 × 5/100)
⇒ $8500 = P (1 + 25/100)
⇒ $8500 = P (100 + 25/100)
⇒ $8500 = P × 125/100
⇒ P × 125/100 = $8500
⇒ P = 8500/125/100
⇒ P = 8500 × 100/125
⇒ P = 8500 × 100/125
⇒ P = 850000/125
⇒ P = $6800
Thus, the sum borrowed (P) = $6800 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 8500, then the Principal = 100/125 × 8500
= 100 × 8500/125
= 850000/125
= 6800
Thus, Principal = $6800
Thus, the sum borrowed = $6800 Answer
Similar Questions
(1) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 10% simple interest?
(2) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(3) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 3 years.
(6) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?
(7) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(8) If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?
(10) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.