Question:
Lisa had to pay $4536 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
$4050
Solution And Explanation
Solution
Given,
Amount (A) = $4536
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
$4536 = P (1 + 4% × 3)
⇒ $4536 = P (1 + 4/100 × 3)
⇒ $4536 = P (1 + 4 × 3/100)
⇒ $4536 = P (1 + 12/100)
⇒ $4536 = P (100 + 12/100)
⇒ $4536 = P × 112/100
⇒ P × 112/100 = $4536
⇒ P = 4536/112/100
⇒ P = 4536 × 100/112
⇒ P = 4536 × 100/112
⇒ P = 453600/112
⇒ P = $4050
Thus, the sum borrowed (P) = $4050 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 4536, then the Principal = 100/112 × 4536
= 100 × 4536/112
= 453600/112
= 4050
Thus, Principal = $4050
Thus, the sum borrowed = $4050 Answer
Similar Questions
(1) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 3 years.
(2) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 8% simple interest?
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.
(4) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10860 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(6) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?
(7) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 6% simple interest?
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 8 years.
(9) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?
(10) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.