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) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 4 years.
(3) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.
(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?
(6) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 8 years.
(9) How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?
(10) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?