Question:
How much loan did Edward borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9500 to clear it?
Correct Answer
$7600
Solution And Explanation
Solution
Given,
Amount (A) = $9500
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
$9500 = P (1 + 5% × 5)
⇒ $9500 = P (1 + 5/100 × 5)
⇒ $9500 = P (1 + 5 × 5/100)
⇒ $9500 = P (1 + 25/100)
⇒ $9500 = P (100 + 25/100)
⇒ $9500 = P × 125/100
⇒ P × 125/100 = $9500
⇒ P = 9500/125/100
⇒ P = 9500 × 100/125
⇒ P = 9500 × 100/125
⇒ P = 950000/125
⇒ P = $7600
Thus, the sum borrowed (P) = $7600 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 9500, then the Principal = 100/125 × 9500
= 100 × 9500/125
= 950000/125
= 7600
Thus, Principal = $7600
Thus, the sum borrowed = $7600 Answer
Similar Questions
(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 8 years.
(2) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
(4) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 4 years.
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.
(7) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 3 years.
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 3 years.
(9) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 4% simple interest?
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.