Question:
Karen had to pay $4424 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
$3950
Solution And Explanation
Solution
Given,
Amount (A) = $4424
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
$4424 = P (1 + 4% × 3)
⇒ $4424 = P (1 + 4/100 × 3)
⇒ $4424 = P (1 + 4 × 3/100)
⇒ $4424 = P (1 + 12/100)
⇒ $4424 = P (100 + 12/100)
⇒ $4424 = P × 112/100
⇒ P × 112/100 = $4424
⇒ P = 4424/112/100
⇒ P = 4424 × 100/112
⇒ P = 4424 × 100/112
⇒ P = 442400/112
⇒ P = $3950
Thus, the sum borrowed (P) = $3950 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 4424, then the Principal = 100/112 × 4424
= 100 × 4424/112
= 442400/112
= 3950
Thus, Principal = $3950
Thus, the sum borrowed = $3950 Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.
(2) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?
(3) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8791 to clear the loan, then find the time period of the loan.
(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 8% simple interest?
(5) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.
(6) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.
(7) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(8) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(9) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.