Question:
How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?
Correct Answer
$7700
Solution And Explanation
Solution
Given,
Amount (A) = $9625
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
$9625 = P (1 + 5% × 5)
⇒ $9625 = P (1 + 5/100 × 5)
⇒ $9625 = P (1 + 5 × 5/100)
⇒ $9625 = P (1 + 25/100)
⇒ $9625 = P (100 + 25/100)
⇒ $9625 = P × 125/100
⇒ P × 125/100 = $9625
⇒ P = 9625/125/100
⇒ P = 9625 × 100/125
⇒ P = 9625 × 100/125
⇒ P = 962500/125
⇒ P = $7700
Thus, the sum borrowed (P) = $7700 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 9625, then the Principal = 100/125 × 9625
= 100 × 9625/125
= 962500/125
= 7700
Thus, Principal = $7700
Thus, the sum borrowed = $7700 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 3 years.
(3) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?
(4) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 4% simple interest?
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 7 years.
(6) If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?
(8) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(10) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 5% simple interest?