Question:
James had to pay $3360 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
$3000
Solution And Explanation
Solution
Given,
Amount (A) = $3360
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
$3360 = P (1 + 4% × 3)
⇒ $3360 = P (1 + 4/100 × 3)
⇒ $3360 = P (1 + 4 × 3/100)
⇒ $3360 = P (1 + 12/100)
⇒ $3360 = P (100 + 12/100)
⇒ $3360 = P × 112/100
⇒ P × 112/100 = $3360
⇒ P = 3360/112/100
⇒ P = 3360 × 100/112
⇒ P = 3360 × 100/112
⇒ P = 336000/112
⇒ P = $3000
Thus, the sum borrowed (P) = $3000 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 3360, then the Principal = 100/112 × 3360
= 100 × 3360/112
= 336000/112
= 3000
Thus, Principal = $3000
Thus, the sum borrowed = $3000 Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.
(2) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
(3) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.
(4) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(5) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 3 years.
(8) If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 8 years.