Question:
Mary had to pay $3416 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
$3050
Solution And Explanation
Solution
Given,
Amount (A) = $3416
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
$3416 = P (1 + 4% × 3)
⇒ $3416 = P (1 + 4/100 × 3)
⇒ $3416 = P (1 + 4 × 3/100)
⇒ $3416 = P (1 + 12/100)
⇒ $3416 = P (100 + 12/100)
⇒ $3416 = P × 112/100
⇒ P × 112/100 = $3416
⇒ P = 3416/112/100
⇒ P = 3416 × 100/112
⇒ P = 3416 × 100/112
⇒ P = 341600/112
⇒ P = $3050
Thus, the sum borrowed (P) = $3050 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 3416, then the Principal = 100/112 × 3416
= 100 × 3416/112
= 341600/112
= 3050
Thus, Principal = $3050
Thus, the sum borrowed = $3050 Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 3 years.
(2) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?
(3) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?
(4) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 7% simple interest?
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.
(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 4 years.
(7) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(9) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $11000 to clear the loan, then find the time period of the loan.