Question:
How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?
Correct Answer
$5850
Solution And Explanation
Solution
Given,
Amount (A) = $7312.5
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
$7312.5 = P (1 + 5% × 5)
⇒ $7312.5 = P (1 + 5/100 × 5)
⇒ $7312.5 = P (1 + 5 × 5/100)
⇒ $7312.5 = P (1 + 25/100)
⇒ $7312.5 = P (100 + 25/100)
⇒ $7312.5 = P × 125/100
⇒ P × 125/100 = $7312.5
⇒ P = 7312.5/125/100
⇒ P = 7312.5 × 100/125
⇒ P = 7312.5 × 100/125
⇒ P = 731250/125
⇒ P = $5850
Thus, the sum borrowed (P) = $5850 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 7312.5, then the Principal = 100/125 × 7312.5
= 100 × 7312.5/125
= 731250/125
= 5850
Thus, Principal = $5850
Thus, the sum borrowed = $5850 Answer
Similar Questions
(1) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.
(3) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 8% simple interest?
(4) What amount will be due after 2 years if John borrowed a sum of $3100 at a 6% simple interest?
(5) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(6) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.
(8) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
(10) How much loan did Joshua borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8280 to clear it?