Question:
Barbara had to pay $3869.5 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
$3550
Solution And Explanation
Solution
Given,
Amount (A) = $3869.5
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
$3869.5 = P (1 + 3% × 3)
⇒ $3869.5 = P (1 + 3/100 × 3)
⇒ $3869.5 = P (1 + 3 × 3/100)
⇒ $3869.5 = P (1 + 9/100)
⇒ $3869.5 = P (100 + 9/100)
⇒ $3869.5 = P × 109/100
⇒ P × 109/100 = $3869.5
⇒ P = 3869.5/109/100
⇒ P = 3869.5 × 100/109
⇒ P = 3869.5 × 100/109
⇒ P = 386950/109
⇒ 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 = 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 3869.5, then the Principal = 100/109 × 3869.5
= 100 × 3869.5/109
= 386950/109
= 3550
Thus, Principal = $3550
Thus, the sum borrowed = $3550 Answer
Similar Questions
(1) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 3 years.
(2) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.
(4) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?
(5) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7421 to clear the loan, then find the time period of the loan.
(7) What amount does John have to pay after 6 years if he takes a loan of $3200 at 7% simple interest?
(8) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?
(9) How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?
(10) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.