Question:
How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?
Correct Answer
$5350
Solution And Explanation
Solution
Given,
Amount (A) = $6687.5
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
$6687.5 = P (1 + 5% × 5)
⇒ $6687.5 = P (1 + 5/100 × 5)
⇒ $6687.5 = P (1 + 5 × 5/100)
⇒ $6687.5 = P (1 + 25/100)
⇒ $6687.5 = P (100 + 25/100)
⇒ $6687.5 = P × 125/100
⇒ P × 125/100 = $6687.5
⇒ P = 6687.5/125/100
⇒ P = 6687.5 × 100/125
⇒ P = 6687.5 × 100/125
⇒ P = 668750/125
⇒ P = $5350
Thus, the sum borrowed (P) = $5350 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 6687.5, then the Principal = 100/125 × 6687.5
= 100 × 6687.5/125
= 668750/125
= 5350
Thus, Principal = $5350
Thus, the sum borrowed = $5350 Answer
Similar Questions
(1) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
(3) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 5% simple interest?
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.
(5) How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?
(6) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.
(7) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.
(9) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 2% simple interest?
(10) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 10% simple interest?