Question : David had to pay $3604 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 $3400
Solution & Explanation
Solution
Given,
Amount (A) = $3604
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
$3604 = P (1 + 2% × 3)
⇒ $3604 = P (1 + 2/100 × 3)
⇒ $3604 = P (1 + 2 × 3/100)
⇒ $3604 = P (1 + 6/100)
⇒ $3604 = P (100 + 6/100)
⇒ $3604 = P × 106/100
⇒ P × 106/100 = $3604
⇒ P = 3604/106/100
⇒ P = 3604 × 100/106
⇒ P = 3604 × 100/106
⇒ P = 360400/106
⇒ P = $3400
Thus, the sum borrowed (P) = $3400 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 3604, then the Principal = 100/106 × 3604
= 100 × 3604/106
= 360400/106
= 3400
Thus, Principal = $3400
Thus, the sum borrowed = $3400 Answer
Similar Questions
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.
(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 3% simple interest?
(5) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?
(6) In how much time a principal of $3150 will amount to $3276 at a simple interest of 2% per annum?
(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?