Question:
Nancy had to pay $4523.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
Correct Answer
$4150
Solution And Explanation
Solution
Given,
Amount (A) = $4523.5
Rate of Simple Interest (R) = 3%
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
$4523.5 = P (1 + 3% × 3)
⇒ $4523.5 = P (1 + 3/100 × 3)
⇒ $4523.5 = P (1 + 3 × 3/100)
⇒ $4523.5 = P (1 + 9/100)
⇒ $4523.5 = P (100 + 9/100)
⇒ $4523.5 = P × 109/100
⇒ P × 109/100 = $4523.5
⇒ P = 4523.5/109/100
⇒ P = 4523.5 × 100/109
⇒ P = 4523.5 × 100/109
⇒ P = 452350/109
⇒ P = $4150
Thus, the sum borrowed (P) = $4150 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 4523.5, then the Principal = 100/109 × 4523.5
= 100 × 4523.5/109
= 452350/109
= 4150
Thus, Principal = $4150
Thus, the sum borrowed = $4150 Answer
Similar Questions
(1) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 4 years.
(2) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.
(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 7% simple interest?
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.
(5) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(6) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?
(7) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 8 years.
(8) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(9) If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?