Question:
Charles had to pay $4134 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
$3900
Solution And Explanation
Solution
Given,
Amount (A) = $4134
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
$4134 = P (1 + 2% × 3)
⇒ $4134 = P (1 + 2/100 × 3)
⇒ $4134 = P (1 + 2 × 3/100)
⇒ $4134 = P (1 + 6/100)
⇒ $4134 = P (100 + 6/100)
⇒ $4134 = P × 106/100
⇒ P × 106/100 = $4134
⇒ P = 4134/106/100
⇒ P = 4134 × 100/106
⇒ P = 4134 × 100/106
⇒ P = 413400/106
⇒ P = $3900
Thus, the sum borrowed (P) = $3900 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 4134, then the Principal = 100/106 × 4134
= 100 × 4134/106
= 413400/106
= 3900
Thus, Principal = $3900
Thus, the sum borrowed = $3900 Answer
Similar Questions
(1) In how much time a principal of $3150 will amount to $3528 at a simple interest of 3% per annum?
(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.
(3) Jennifer had to pay $3640 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 5% simple interest?
(5) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if David borrowed a sum of $3200 at a 7% simple interest?
(7) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
(8) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(9) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(10) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 4 years.