Question:
Betty had to pay $4760 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
Correct Answer
$4250
Solution And Explanation
Solution
Given,
Amount (A) = $4760
Rate of Simple Interest (R) = 4%
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
$4760 = P (1 + 4% × 3)
⇒ $4760 = P (1 + 4/100 × 3)
⇒ $4760 = P (1 + 4 × 3/100)
⇒ $4760 = P (1 + 12/100)
⇒ $4760 = P (100 + 12/100)
⇒ $4760 = P × 112/100
⇒ P × 112/100 = $4760
⇒ P = 4760/112/100
⇒ P = 4760 × 100/112
⇒ P = 4760 × 100/112
⇒ P = 476000/112
⇒ P = $4250
Thus, the sum borrowed (P) = $4250 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 12
Thus, simple interest for 3 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 4760, then the Principal = 100/112 × 4760
= 100 × 4760/112
= 476000/112
= 4250
Thus, Principal = $4250
Thus, the sum borrowed = $4250 Answer
Similar Questions
(1) 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.
(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.
(4) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(5) How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?
(6) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?
(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 7 years.
(8) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
(9) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(10) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 3 years.