Question:
Sandra had to pay $4984 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
$4450
Solution And Explanation
Solution
Given,
Amount (A) = $4984
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
$4984 = P (1 + 4% × 3)
⇒ $4984 = P (1 + 4/100 × 3)
⇒ $4984 = P (1 + 4 × 3/100)
⇒ $4984 = P (1 + 12/100)
⇒ $4984 = P (100 + 12/100)
⇒ $4984 = P × 112/100
⇒ P × 112/100 = $4984
⇒ P = 4984/112/100
⇒ P = 4984 × 100/112
⇒ P = 4984 × 100/112
⇒ P = 498400/112
⇒ P = $4450
Thus, the sum borrowed (P) = $4450 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 4984, then the Principal = 100/112 × 4984
= 100 × 4984/112
= 498400/112
= 4450
Thus, Principal = $4450
Thus, the sum borrowed = $4450 Answer
Similar Questions
(1) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(2) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.
(4) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(5) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.
(6) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9060 to clear it?
(7) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 10% simple interest?
(9) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 3 years.
(10) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.