Question:
Mark had to pay $4928 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
$4400
Solution And Explanation
Solution
Given,
Amount (A) = $4928
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
$4928 = P (1 + 4% × 3)
⇒ $4928 = P (1 + 4/100 × 3)
⇒ $4928 = P (1 + 4 × 3/100)
⇒ $4928 = P (1 + 12/100)
⇒ $4928 = P (100 + 12/100)
⇒ $4928 = P × 112/100
⇒ P × 112/100 = $4928
⇒ P = 4928/112/100
⇒ P = 4928 × 100/112
⇒ P = 4928 × 100/112
⇒ P = 492800/112
⇒ P = $4400
Thus, the sum borrowed (P) = $4400 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 4928, then the Principal = 100/112 × 4928
= 100 × 4928/112
= 492800/112
= 4400
Thus, Principal = $4400
Thus, the sum borrowed = $4400 Answer
Similar Questions
(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.
(2) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.
(4) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(5) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 4 years.
(7) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.
(9) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(10) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.