Question:
Thomas had to pay $4142 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
$3800
Solution And Explanation
Solution
Given,
Amount (A) = $4142
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
$4142 = P (1 + 3% × 3)
⇒ $4142 = P (1 + 3/100 × 3)
⇒ $4142 = P (1 + 3 × 3/100)
⇒ $4142 = P (1 + 9/100)
⇒ $4142 = P (100 + 9/100)
⇒ $4142 = P × 109/100
⇒ P × 109/100 = $4142
⇒ P = 4142/109/100
⇒ P = 4142 × 100/109
⇒ P = 4142 × 100/109
⇒ P = 414200/109
⇒ P = $3800
Thus, the sum borrowed (P) = $3800 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 4142, then the Principal = 100/109 × 4142
= 100 × 4142/109
= 414200/109
= 3800
Thus, Principal = $3800
Thus, the sum borrowed = $3800 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(2) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(3) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?
(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
(5) If Sarah paid $4466 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?
(7) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?
(9) Emily had to pay $5462.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.