Question:
How much loan did Nancy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7687.5 to clear it?
Correct Answer
$6150
Solution And Explanation
Solution
Given,
Amount (A) = $7687.5
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
$7687.5 = P (1 + 5% × 5)
⇒ $7687.5 = P (1 + 5/100 × 5)
⇒ $7687.5 = P (1 + 5 × 5/100)
⇒ $7687.5 = P (1 + 25/100)
⇒ $7687.5 = P (100 + 25/100)
⇒ $7687.5 = P × 125/100
⇒ P × 125/100 = $7687.5
⇒ P = 7687.5/125/100
⇒ P = 7687.5 × 100/125
⇒ P = 7687.5 × 100/125
⇒ P = 768750/125
⇒ P = $6150
Thus, the sum borrowed (P) = $6150 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 7687.5, then the Principal = 100/125 × 7687.5
= 100 × 7687.5/125
= 768750/125
= 6150
Thus, Principal = $6150
Thus, the sum borrowed = $6150 Answer
Similar Questions
(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.
(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.
(3) How much loan did Donna borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8220 to clear it?
(4) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.
(5) If Linda paid $3886 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?
(7) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.
(8) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 8 years.
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 7 years.