Question:
Thomas had to pay $4256 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
$3800
Solution And Explanation
Solution
Given,
Amount (A) = $4256
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
$4256 = P (1 + 4% × 3)
⇒ $4256 = P (1 + 4/100 × 3)
⇒ $4256 = P (1 + 4 × 3/100)
⇒ $4256 = P (1 + 12/100)
⇒ $4256 = P (100 + 12/100)
⇒ $4256 = P × 112/100
⇒ P × 112/100 = $4256
⇒ P = 4256/112/100
⇒ P = 4256 × 100/112
⇒ P = 4256 × 100/112
⇒ P = 425600/112
⇒ P = $3800
Thus, the sum borrowed (P) = $3800 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 4256, then the Principal = 100/112 × 4256
= 100 × 4256/112
= 425600/112
= 3800
Thus, Principal = $3800
Thus, the sum borrowed = $3800 Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?
(3) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(4) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 4% simple interest?
(5) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.
(8) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
(9) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
(10) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.