Question:
How much loan did Thomas borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7250 to clear it?
Correct Answer
$5800
Solution And Explanation
Solution
Given,
Amount (A) = $7250
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
$7250 = P (1 + 5% × 5)
⇒ $7250 = P (1 + 5/100 × 5)
⇒ $7250 = P (1 + 5 × 5/100)
⇒ $7250 = P (1 + 25/100)
⇒ $7250 = P (100 + 25/100)
⇒ $7250 = P × 125/100
⇒ P × 125/100 = $7250
⇒ P = 7250/125/100
⇒ P = 7250 × 100/125
⇒ P = 7250 × 100/125
⇒ P = 725000/125
⇒ P = $5800
Thus, the sum borrowed (P) = $5800 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 7250, then the Principal = 100/125 × 7250
= 100 × 7250/125
= 725000/125
= 5800
Thus, Principal = $5800
Thus, the sum borrowed = $5800 Answer
Similar Questions
(1) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.
(2) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10136 to clear the loan, then find the time period of the loan.
(3) How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?
(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?
(5) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.
(7) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 4 years.
(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.
(9) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 3 years.
(10) How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?