Question:
Paul had to pay $5123 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
$4700
Solution And Explanation
Solution
Given,
Amount (A) = $5123
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
$5123 = P (1 + 3% × 3)
⇒ $5123 = P (1 + 3/100 × 3)
⇒ $5123 = P (1 + 3 × 3/100)
⇒ $5123 = P (1 + 9/100)
⇒ $5123 = P (100 + 9/100)
⇒ $5123 = P × 109/100
⇒ P × 109/100 = $5123
⇒ P = 5123/109/100
⇒ P = 5123 × 100/109
⇒ P = 5123 × 100/109
⇒ P = 512300/109
⇒ P = $4700
Thus, the sum borrowed (P) = $4700 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 5123, then the Principal = 100/109 × 5123
= 100 × 5123/109
= 512300/109
= 4700
Thus, Principal = $4700
Thus, the sum borrowed = $4700 Answer
Similar Questions
(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.
(2) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?
(3) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?
(4) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.
(5) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 3 years.
(6) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.
(8) How much loan did Steven borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7590 to clear it?
(9) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?
(10) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?