Question:
Steven had to pay $5014 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
Correct Answer
$4600
Solution And Explanation
Solution
Given,
Amount (A) = $5014
Rate of Simple Interest (R) = 3%
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
$5014 = P (1 + 3% × 3)
⇒ $5014 = P (1 + 3/100 × 3)
⇒ $5014 = P (1 + 3 × 3/100)
⇒ $5014 = P (1 + 9/100)
⇒ $5014 = P (100 + 9/100)
⇒ $5014 = P × 109/100
⇒ P × 109/100 = $5014
⇒ P = 5014/109/100
⇒ P = 5014 × 100/109
⇒ P = 5014 × 100/109
⇒ P = 501400/109
⇒ P = $4600
Thus, the sum borrowed (P) = $4600 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 5014, then the Principal = 100/109 × 5014
= 100 × 5014/109
= 501400/109
= 4600
Thus, Principal = $4600
Thus, the sum borrowed = $4600 Answer
Similar Questions
(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 7 years.
(2) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 8 years.
(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 3 years.
(5) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?
(7) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3000 will amount to $3300 at a simple interest of 5% per annum?
(9) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 7% simple interest?
(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.