Question:
Linda had to pay $3752 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
$3350
Solution And Explanation
Solution
Given,
Amount (A) = $3752
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
$3752 = P (1 + 4% × 3)
⇒ $3752 = P (1 + 4/100 × 3)
⇒ $3752 = P (1 + 4 × 3/100)
⇒ $3752 = P (1 + 12/100)
⇒ $3752 = P (100 + 12/100)
⇒ $3752 = P × 112/100
⇒ P × 112/100 = $3752
⇒ P = 3752/112/100
⇒ P = 3752 × 100/112
⇒ P = 3752 × 100/112
⇒ P = 375200/112
⇒ P = $3350
Thus, the sum borrowed (P) = $3350 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 3752, then the Principal = 100/112 × 3752
= 100 × 3752/112
= 375200/112
= 3350
Thus, Principal = $3350
Thus, the sum borrowed = $3350 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.
(2) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 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 6% simple interest for 8 years.
(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 7 years.
(5) How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?
(6) In how much time a principal of $3150 will amount to $3276 at a simple interest of 2% per annum?
(7) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(9) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?