Question:
Matthew had to pay $4704 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
$4200
Solution And Explanation
Solution
Given,
Amount (A) = $4704
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
$4704 = P (1 + 4% × 3)
⇒ $4704 = P (1 + 4/100 × 3)
⇒ $4704 = P (1 + 4 × 3/100)
⇒ $4704 = P (1 + 12/100)
⇒ $4704 = P (100 + 12/100)
⇒ $4704 = P × 112/100
⇒ P × 112/100 = $4704
⇒ P = 4704/112/100
⇒ P = 4704 × 100/112
⇒ P = 4704 × 100/112
⇒ P = 470400/112
⇒ P = $4200
Thus, the sum borrowed (P) = $4200 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 4704, then the Principal = 100/112 × 4704
= 100 × 4704/112
= 470400/112
= 4200
Thus, Principal = $4200
Thus, the sum borrowed = $4200 Answer
Similar Questions
(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.
(2) Daniel had to pay $4469 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?
(4) If Elizabeth borrowed $3450 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.
(8) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?
(9) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 5% simple interest?
(10) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?