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) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.
(2) How much loan did Patricia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6180 to clear it?
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 8 years.
(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 4 years.
(5) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.
(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 7% simple interest?
(8) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.
(9) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.
(10) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.