Question:
How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?
Correct Answer
$5250
Solution And Explanation
Solution
Given,
Amount (A) = $5775
Rate of Simple Interest (R) = 2%
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
$5775 = P (1 + 2% × 5)
⇒ $5775 = P (1 + 2/100 × 5)
⇒ $5775 = P (1 + 2 × 5/100)
⇒ $5775 = P (1 + 10/100)
⇒ $5775 = P (100 + 10/100)
⇒ $5775 = P × 110/100
⇒ P × 110/100 = $5775
⇒ P = 5775/110/100
⇒ P = 5775 × 100/110
⇒ P = 5775 × 100/110
⇒ P = 577500/110
⇒ P = $5250
Thus, the sum borrowed (P) = $5250 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 5775, then the Principal = 100/110 × 5775
= 100 × 5775/110
= 577500/110
= 5250
Thus, Principal = $5250
Thus, the sum borrowed = $5250 Answer
Similar Questions
(1) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.
(3) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.
(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?
(6) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?
(7) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.
(8) Robert had to pay $3472 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 10% simple interest?
(10) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?