Question:
How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
Correct Answer
$7100
Solution And Explanation
Solution
Given,
Amount (A) = $8875
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
$8875 = P (1 + 5% × 5)
⇒ $8875 = P (1 + 5/100 × 5)
⇒ $8875 = P (1 + 5 × 5/100)
⇒ $8875 = P (1 + 25/100)
⇒ $8875 = P (100 + 25/100)
⇒ $8875 = P × 125/100
⇒ P × 125/100 = $8875
⇒ P = 8875/125/100
⇒ P = 8875 × 100/125
⇒ P = 8875 × 100/125
⇒ P = 887500/125
⇒ P = $7100
Thus, the sum borrowed (P) = $7100 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 8875, then the Principal = 100/125 × 8875
= 100 × 8875/125
= 887500/125
= 7100
Thus, Principal = $7100
Thus, the sum borrowed = $7100 Answer
Similar Questions
(1) If Sarah borrowed $3850 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(2) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?
(3) In how much time a principal of $3000 will amount to $3300 at a simple interest of 5% per annum?
(4) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.
(5) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?
(6) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(8) 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?
(9) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.