Question:
How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?
Correct Answer
$7950
Solution And Explanation
Solution
Given,
Amount (A) = $9937.5
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
$9937.5 = P (1 + 5% × 5)
⇒ $9937.5 = P (1 + 5/100 × 5)
⇒ $9937.5 = P (1 + 5 × 5/100)
⇒ $9937.5 = P (1 + 25/100)
⇒ $9937.5 = P (100 + 25/100)
⇒ $9937.5 = P × 125/100
⇒ P × 125/100 = $9937.5
⇒ P = 9937.5/125/100
⇒ P = 9937.5 × 100/125
⇒ P = 9937.5 × 100/125
⇒ P = 993750/125
⇒ P = $7950
Thus, the sum borrowed (P) = $7950 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 9937.5, then the Principal = 100/125 × 9937.5
= 100 × 9937.5/125
= 993750/125
= 7950
Thus, Principal = $7950
Thus, the sum borrowed = $7950 Answer
Similar Questions
(1) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 7 years.
(2) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?
(3) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.
(4) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?
(5) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.
(6) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 8 years.
(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 4 years.
(10) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.