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) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
(2) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9180 to clear it?
(3) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 9% simple interest?
(4) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 8% simple interest?
(5) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12670 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.
(7) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?
(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 7% simple interest?
(9) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 3 years.