Question:
John had to pay $3584 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
$3200
Solution And Explanation
Solution
Given,
Amount (A) = $3584
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
$3584 = P (1 + 4% × 3)
⇒ $3584 = P (1 + 4/100 × 3)
⇒ $3584 = P (1 + 4 × 3/100)
⇒ $3584 = P (1 + 12/100)
⇒ $3584 = P (100 + 12/100)
⇒ $3584 = P × 112/100
⇒ P × 112/100 = $3584
⇒ P = 3584/112/100
⇒ P = 3584 × 100/112
⇒ P = 3584 × 100/112
⇒ P = 358400/112
⇒ P = $3200
Thus, the sum borrowed (P) = $3200 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 3584, then the Principal = 100/112 × 3584
= 100 × 3584/112
= 358400/112
= 3200
Thus, Principal = $3200
Thus, the sum borrowed = $3200 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(2) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?
(3) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.
(4) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.
(6) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10136 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 4 years.
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 7 years.
(9) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.
(10) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 5% simple interest?