Question:
John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
Correct Answer
$3200
Solution And Explanation
Solution
Given,
Amount (A) = $3392
Rate of Simple Interest (R) = 2%
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
$3392 = P (1 + 2% × 3)
⇒ $3392 = P (1 + 2/100 × 3)
⇒ $3392 = P (1 + 2 × 3/100)
⇒ $3392 = P (1 + 6/100)
⇒ $3392 = P (100 + 6/100)
⇒ $3392 = P × 106/100
⇒ P × 106/100 = $3392
⇒ P = 3392/106/100
⇒ P = 3392 × 100/106
⇒ P = 3392 × 100/106
⇒ P = 339200/106
⇒ 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 6
Thus, simple interest for 3 years = 6
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 6 = 106
Calculation of the Principal
Now,
∵ If the Amount is 106, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/106
∴ If the Amount is 3392, then the Principal = 100/106 × 3392
= 100 × 3392/106
= 339200/106
= 3200
Thus, Principal = $3200
Thus, the sum borrowed = $3200 Answer
Similar Questions
(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.
(2) How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?
(3) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?
(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 3 years.
(5) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 4% simple interest?
(6) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.
(7) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.
(9) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?
(10) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.