Question:
Barbara had to pay $3763 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
$3550
Solution And Explanation
Solution
Given,
Amount (A) = $3763
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
$3763 = P (1 + 2% × 3)
⇒ $3763 = P (1 + 2/100 × 3)
⇒ $3763 = P (1 + 2 × 3/100)
⇒ $3763 = P (1 + 6/100)
⇒ $3763 = P (100 + 6/100)
⇒ $3763 = P × 106/100
⇒ P × 106/100 = $3763
⇒ P = 3763/106/100
⇒ P = 3763 × 100/106
⇒ P = 3763 × 100/106
⇒ P = 376300/106
⇒ P = $3550
Thus, the sum borrowed (P) = $3550 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 3763, then the Principal = 100/106 × 3763
= 100 × 3763/106
= 376300/106
= 3550
Thus, Principal = $3550
Thus, the sum borrowed = $3550 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(2) What amount will be due after 2 years if James borrowed a sum of $3000 at a 10% simple interest?
(3) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 8% simple interest?
(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 8% simple interest?
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.
(6) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 8 years.
(8) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?
(9) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(10) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 7% simple interest?