Question:
How much loan did Betty borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7812.5 to clear it?
Correct Answer
$6250
Solution And Explanation
Solution
Given,
Amount (A) = $7812.5
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
$7812.5 = P (1 + 5% × 5)
⇒ $7812.5 = P (1 + 5/100 × 5)
⇒ $7812.5 = P (1 + 5 × 5/100)
⇒ $7812.5 = P (1 + 25/100)
⇒ $7812.5 = P (100 + 25/100)
⇒ $7812.5 = P × 125/100
⇒ P × 125/100 = $7812.5
⇒ P = 7812.5/125/100
⇒ P = 7812.5 × 100/125
⇒ P = 7812.5 × 100/125
⇒ P = 781250/125
⇒ P = $6250
Thus, the sum borrowed (P) = $6250 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 7812.5, then the Principal = 100/125 × 7812.5
= 100 × 7812.5/125
= 781250/125
= 6250
Thus, Principal = $6250
Thus, the sum borrowed = $6250 Answer
Similar Questions
(1) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 7% simple interest?
(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
(4) 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?
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 4 years.
(6) What amount does John have to pay after 5 years if he takes a loan of $3200 at 8% simple interest?
(7) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 4 years.
(9) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.
(10) 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?