Question:
Nancy had to pay $4399 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
$4150
Solution And Explanation
Solution
Given,
Amount (A) = $4399
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
$4399 = P (1 + 2% × 3)
⇒ $4399 = P (1 + 2/100 × 3)
⇒ $4399 = P (1 + 2 × 3/100)
⇒ $4399 = P (1 + 6/100)
⇒ $4399 = P (100 + 6/100)
⇒ $4399 = P × 106/100
⇒ P × 106/100 = $4399
⇒ P = 4399/106/100
⇒ P = 4399 × 100/106
⇒ P = 4399 × 100/106
⇒ P = 439900/106
⇒ 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 = 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 4399, then the Principal = 100/106 × 4399
= 100 × 4399/106
= 439900/106
= 4150
Thus, Principal = $4150
Thus, the sum borrowed = $4150 Answer
Similar Questions
(1) How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 8 years.
(3) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 4 years.
(5) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.
(6) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?
(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?
(8) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?
(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.
(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 8 years.