Question:
How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?
Correct Answer
$5700
Solution And Explanation
Solution
Given,
Amount (A) = $7125
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
$7125 = P (1 + 5% × 5)
⇒ $7125 = P (1 + 5/100 × 5)
⇒ $7125 = P (1 + 5 × 5/100)
⇒ $7125 = P (1 + 25/100)
⇒ $7125 = P (100 + 25/100)
⇒ $7125 = P × 125/100
⇒ P × 125/100 = $7125
⇒ P = 7125/125/100
⇒ P = 7125 × 100/125
⇒ P = 7125 × 100/125
⇒ P = 712500/125
⇒ P = $5700
Thus, the sum borrowed (P) = $5700 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 7125, then the Principal = 100/125 × 7125
= 100 × 7125/125
= 712500/125
= 5700
Thus, Principal = $5700
Thus, the sum borrowed = $5700 Answer
Similar Questions
(1) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.
(2) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.
(3) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6724 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(5) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 3 years.
(6) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(7) Jessica had to pay $4087.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) What amount does William have to pay after 6 years if he takes a loan of $3500 at 3% simple interest?
(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 6% simple interest?
(10) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?