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) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.
(2) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 6% simple interest?
(3) If Sarah borrowed $3850 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 3 years.
(5) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.
(6) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) What amount does William have to pay after 5 years if he takes a loan of $3500 at 2% simple interest?
(8) How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 7 years.