Question:
Sarah had to pay $4312 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
$3850
Solution And Explanation
Solution
Given,
Amount (A) = $4312
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
$4312 = P (1 + 4% × 3)
⇒ $4312 = P (1 + 4/100 × 3)
⇒ $4312 = P (1 + 4 × 3/100)
⇒ $4312 = P (1 + 12/100)
⇒ $4312 = P (100 + 12/100)
⇒ $4312 = P × 112/100
⇒ P × 112/100 = $4312
⇒ P = 4312/112/100
⇒ P = 4312 × 100/112
⇒ P = 4312 × 100/112
⇒ P = 431200/112
⇒ P = $3850
Thus, the sum borrowed (P) = $3850 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 4312, then the Principal = 100/112 × 4312
= 100 × 4312/112
= 431200/112
= 3850
Thus, Principal = $3850
Thus, the sum borrowed = $3850 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(2) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.
(3) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 8 years.
(6) What amount does William have to pay after 6 years if he takes a loan of $3500 at 8% simple interest?
(7) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 4 years.
(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.
(10) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.