Question:
John had to pay $3488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
Correct Answer
$3200
Solution And Explanation
Solution
Given,
Amount (A) = $3488
Rate of Simple Interest (R) = 3%
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
$3488 = P (1 + 3% × 3)
⇒ $3488 = P (1 + 3/100 × 3)
⇒ $3488 = P (1 + 3 × 3/100)
⇒ $3488 = P (1 + 9/100)
⇒ $3488 = P (100 + 9/100)
⇒ $3488 = P × 109/100
⇒ P × 109/100 = $3488
⇒ P = 3488/109/100
⇒ P = 3488 × 100/109
⇒ P = 3488 × 100/109
⇒ P = 348800/109
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 3488, then the Principal = 100/109 × 3488
= 100 × 3488/109
= 348800/109
= 3200
Thus, Principal = $3200
Thus, the sum borrowed = $3200 Answer
Similar Questions
(1) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 4% simple interest?
(2) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
(3) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
(4) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.
(5) How much loan did Thomas borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6380 to clear it?
(6) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?
(7) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(8) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 6% simple interest?
(9) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 4 years.
(10) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.