Question:
Joseph had to pay $3922 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
$3700
Solution And Explanation
Solution
Given,
Amount (A) = $3922
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
$3922 = P (1 + 2% × 3)
⇒ $3922 = P (1 + 2/100 × 3)
⇒ $3922 = P (1 + 2 × 3/100)
⇒ $3922 = P (1 + 6/100)
⇒ $3922 = P (100 + 6/100)
⇒ $3922 = P × 106/100
⇒ P × 106/100 = $3922
⇒ P = 3922/106/100
⇒ P = 3922 × 100/106
⇒ P = 3922 × 100/106
⇒ P = 392200/106
⇒ P = $3700
Thus, the sum borrowed (P) = $3700 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 3922, then the Principal = 100/106 × 3922
= 100 × 3922/106
= 392200/106
= 3700
Thus, Principal = $3700
Thus, the sum borrowed = $3700 Answer
Similar Questions
(1) How much loan did Patricia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6180 to clear it?
(2) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(3) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 3 years.
(5) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?
(6) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 7% simple interest?
(8) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.
(9) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.