Question:
Thomas had to pay $4028 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
Correct Answer
$3800
Solution And Explanation
Solution
Given,
Amount (A) = $4028
Rate of Simple Interest (R) = 2%
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
$4028 = P (1 + 2% × 3)
⇒ $4028 = P (1 + 2/100 × 3)
⇒ $4028 = P (1 + 2 × 3/100)
⇒ $4028 = P (1 + 6/100)
⇒ $4028 = P (100 + 6/100)
⇒ $4028 = P × 106/100
⇒ P × 106/100 = $4028
⇒ P = 4028/106/100
⇒ P = 4028 × 100/106
⇒ P = 4028 × 100/106
⇒ P = 402800/106
⇒ 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 6
Thus, simple interest for 3 years = 6
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 6 = 106
Calculation of the Principal
Now,
∵ If the Amount is 106, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/106
∴ If the Amount is 4028, then the Principal = 100/106 × 4028
= 100 × 4028/106
= 402800/106
= 3800
Thus, Principal = $3800
Thus, the sum borrowed = $3800 Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 8 years.
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 3 years.
(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.
(4) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.
(5) What amount does William have to pay after 5 years if he takes a loan of $3500 at 9% simple interest?
(6) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(7) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.
(9) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $14000 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.