Question:
Andrew had to pay $5376 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
$4800
Solution And Explanation
Solution
Given,
Amount (A) = $5376
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
$5376 = P (1 + 4% × 3)
⇒ $5376 = P (1 + 4/100 × 3)
⇒ $5376 = P (1 + 4 × 3/100)
⇒ $5376 = P (1 + 12/100)
⇒ $5376 = P (100 + 12/100)
⇒ $5376 = P × 112/100
⇒ P × 112/100 = $5376
⇒ P = 5376/112/100
⇒ P = 5376 × 100/112
⇒ P = 5376 × 100/112
⇒ P = 537600/112
⇒ P = $4800
Thus, the sum borrowed (P) = $4800 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 5376, then the Principal = 100/112 × 5376
= 100 × 5376/112
= 537600/112
= 4800
Thus, Principal = $4800
Thus, the sum borrowed = $4800 Answer
Similar Questions
(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?
(2) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?
(3) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 4% simple interest?
(4) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.
(5) If James borrowed $3000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) 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.
(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?
(8) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.
(9) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 8% simple interest?
(10) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.