Question:
Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
Correct Answer
$3250
Solution And Explanation
Solution
Given,
Amount (A) = $3737.5
Rate of Simple Interest (R) = 5%
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
$3737.5 = P (1 + 5% × 3)
⇒ $3737.5 = P (1 + 5/100 × 3)
⇒ $3737.5 = P (1 + 5 × 3/100)
⇒ $3737.5 = P (1 + 15/100)
⇒ $3737.5 = P (100 + 15/100)
⇒ $3737.5 = P × 115/100
⇒ P × 115/100 = $3737.5
⇒ P = 3737.5/115/100
⇒ P = 3737.5 × 100/115
⇒ P = 3737.5 × 100/115
⇒ P = 373750/115
⇒ P = $3250
Thus, the sum borrowed (P) = $3250 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 15
Thus, simple interest for 3 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 3737.5, then the Principal = 100/115 × 3737.5
= 100 × 3737.5/115
= 373750/115
= 3250
Thus, Principal = $3250
Thus, the sum borrowed = $3250 Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 3 years.
(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.
(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 7 years.
(6) 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.
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 7 years.
(8) In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?
(9) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?
(10) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.