Question:
How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?
Correct Answer
$7900
Solution And Explanation
Solution
Given,
Amount (A) = $9875
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
$9875 = P (1 + 5% × 5)
⇒ $9875 = P (1 + 5/100 × 5)
⇒ $9875 = P (1 + 5 × 5/100)
⇒ $9875 = P (1 + 25/100)
⇒ $9875 = P (100 + 25/100)
⇒ $9875 = P × 125/100
⇒ P × 125/100 = $9875
⇒ P = 9875/125/100
⇒ P = 9875 × 100/125
⇒ P = 9875 × 100/125
⇒ P = 987500/125
⇒ P = $7900
Thus, the sum borrowed (P) = $7900 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 9875, then the Principal = 100/125 × 9875
= 100 × 9875/125
= 987500/125
= 7900
Thus, Principal = $7900
Thus, the sum borrowed = $7900 Answer
Similar Questions
(1) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 4 years.
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 3 years.
(3) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?
(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.
(5) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(7) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(8) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
(9) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.