Question:
Karen had to pay $4305.5 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
$3950
Solution And Explanation
Solution
Given,
Amount (A) = $4305.5
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
$4305.5 = P (1 + 3% × 3)
⇒ $4305.5 = P (1 + 3/100 × 3)
⇒ $4305.5 = P (1 + 3 × 3/100)
⇒ $4305.5 = P (1 + 9/100)
⇒ $4305.5 = P (100 + 9/100)
⇒ $4305.5 = P × 109/100
⇒ P × 109/100 = $4305.5
⇒ P = 4305.5/109/100
⇒ P = 4305.5 × 100/109
⇒ P = 4305.5 × 100/109
⇒ P = 430550/109
⇒ P = $3950
Thus, the sum borrowed (P) = $3950 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 4305.5, then the Principal = 100/109 × 4305.5
= 100 × 4305.5/109
= 430550/109
= 3950
Thus, Principal = $3950
Thus, the sum borrowed = $3950 Answer
Similar Questions
(1) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?
(2) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(3) How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?
(4) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.
(6) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?
(7) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 3 years.
(9) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(10) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 4% simple interest?