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 & 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) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 7 years.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.
(4) What amount will be due after 2 years if William borrowed a sum of $3250 at a 7% simple interest?
(5) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.
(8) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 7% simple interest?
(9) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?