Question:
Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
Correct Answer
$4650
Solution And Explanation
Solution
Given,
Amount (A) = $4929
Rate of Simple Interest (R) = 2%
Time (T) = 3 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
$4929 = P (1 + 2% × 3)
⇒ $4929 = P (1 + 2/100 × 3)
⇒ $4929 = P (1 + 2 × 3/100)
⇒ $4929 = P (1 + 6/100)
⇒ $4929 = P (100 + 6/100)
⇒ $4929 = P × 106/100
⇒ P × 106/100 = $4929
⇒ P = 4929/106/100
⇒ P = 4929 × 100/106
⇒ P = 4929 × 100/106
⇒ P = 492900/106
⇒ P = $4650
Thus, the sum borrowed (P) = $4650 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 = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 2 = 6
Thus, simple interest for 3 years = 6
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 6 = 106
Calculation of the Principal
Now,
∵ If the Amount is 106, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/106
∴ If the Amount is 4929, then the Principal = 100/106 × 4929
= 100 × 4929/106
= 492900/106
= 4650
Thus, Principal = $4650
Thus, the sum borrowed = $4650 Answer
Similar Questions
(1) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.
(3) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?
(4) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(5) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?
(6) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.
(8) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
(9) If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) What amount will be due after 2 years if John borrowed a sum of $3100 at a 4% simple interest?