Question : James had to pay $3180 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 $3000
Solution & Explanation
Solution
Given,
Amount (A) = $3180
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
$3180 = P (1 + 2% × 3)
⇒ $3180 = P (1 + 2/100 × 3)
⇒ $3180 = P (1 + 2 × 3/100)
⇒ $3180 = P (1 + 6/100)
⇒ $3180 = P (100 + 6/100)
⇒ $3180 = P × 106/100
⇒ P × 106/100 = $3180
⇒ P = 3180/106/100
⇒ P = 3180 × 100/106
⇒ P = 3180 × 100/106
⇒ P = 318000/106
⇒ P = $3000
Thus, the sum borrowed (P) = $3000 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 3180, then the Principal = 100/106 × 3180
= 100 × 3180/106
= 318000/106
= 3000
Thus, Principal = $3000
Thus, the sum borrowed = $3000 Answer
Similar Questions
(1) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 8% simple interest?
(2) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?
(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.
(4) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 8% simple interest?
(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 4 years.