Question:
If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3550
Solution And Explanation
Solution
Given,
Amount (A) = $3976
Rate of Simple Interest (R) = 3%
Time (T) = 4 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
$3976 = P (1 + 3% × 4)
⇒ $3976 = P (1 + 3/100 × 4)
⇒ $3976 = P (1 + 3 × 4/100)
⇒ $3976 = P (1 + 12/100)
⇒ $3976 = P (100 + 12/100)
⇒ $3976 = P × 112/100
⇒ P × 112/100 = $3976
⇒ P = 3976/112/100
⇒ P = 3976 × 100/112
⇒ P = 3976 × 100/112
⇒ P = 397600/112
⇒ P = $3550
Thus, the sum borrowed (P) = $3550 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 = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 3 = 12
Thus, simple interest for 4 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 3976, then the Principal = 100/112 × 3976
= 100 × 3976/112
= 397600/112
= 3550
Thus, Principal = $3550
Thus, the sum borrowed = $3550 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?
(2) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 4% simple interest?
(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 3 years.
(5) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 3 years.
(6) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?
(7) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 3 years.
(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.
(10) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.