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) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Patricia had to pay $3433.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 5% simple interest?
(4) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(5) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 3% simple interest?
(6) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 4 years.
(10) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.