Question:
Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
Correct Answer
$4150
Solution And Explanation
Solution
Given,
Amount (A) = $4648
Rate of Simple Interest (R) = 4%
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
$4648 = P (1 + 4% × 3)
⇒ $4648 = P (1 + 4/100 × 3)
⇒ $4648 = P (1 + 4 × 3/100)
⇒ $4648 = P (1 + 12/100)
⇒ $4648 = P (100 + 12/100)
⇒ $4648 = P × 112/100
⇒ P × 112/100 = $4648
⇒ P = 4648/112/100
⇒ P = 4648 × 100/112
⇒ P = 4648 × 100/112
⇒ P = 464800/112
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 12
Thus, simple interest for 3 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 4648, then the Principal = 100/112 × 4648
= 100 × 4648/112
= 464800/112
= 4150
Thus, Principal = $4150
Thus, the sum borrowed = $4150 Answer
Similar Questions
(1) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 4 years.
(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 10% simple interest?
(3) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 6% simple interest?
(4) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 3 years.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.
(6) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 3% simple interest?
(7) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 7 years.
(9) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.
(10) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.