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 And 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) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 3% simple interest?
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.
(4) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.
(5) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 9% simple interest?
(7) How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?
(8) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?
(9) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.