Question:
Jessica had to pay $3975 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
Correct Answer
$3750
Solution And Explanation
Solution
Given,
Amount (A) = $3975
Rate of Simple Interest (R) = 2%
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
$3975 = P (1 + 2% × 3)
⇒ $3975 = P (1 + 2/100 × 3)
⇒ $3975 = P (1 + 2 × 3/100)
⇒ $3975 = P (1 + 6/100)
⇒ $3975 = P (100 + 6/100)
⇒ $3975 = P × 106/100
⇒ P × 106/100 = $3975
⇒ P = 3975/106/100
⇒ P = 3975 × 100/106
⇒ P = 3975 × 100/106
⇒ P = 397500/106
⇒ P = $3750
Thus, the sum borrowed (P) = $3750 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 6
Thus, simple interest for 3 years = 6
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 6 = 106
Calculation of the Principal
Now,
∵ If the Amount is 106, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/106
∴ If the Amount is 3975, then the Principal = 100/106 × 3975
= 100 × 3975/106
= 397500/106
= 3750
Thus, Principal = $3750
Thus, the sum borrowed = $3750 Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.
(2) How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 3 years.
(4) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(5) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 8% simple interest?
(6) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.
(8) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?
(9) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(10) In how much time a principal of $3000 will amount to $3360 at a simple interest of 3% per annum?