Question:
Emily had to pay $5177.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
Correct Answer
$4750
Solution And Explanation
Solution
Given,
Amount (A) = $5177.5
Rate of Simple Interest (R) = 3%
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
$5177.5 = P (1 + 3% × 3)
⇒ $5177.5 = P (1 + 3/100 × 3)
⇒ $5177.5 = P (1 + 3 × 3/100)
⇒ $5177.5 = P (1 + 9/100)
⇒ $5177.5 = P (100 + 9/100)
⇒ $5177.5 = P × 109/100
⇒ P × 109/100 = $5177.5
⇒ P = 5177.5/109/100
⇒ P = 5177.5 × 100/109
⇒ P = 5177.5 × 100/109
⇒ P = 517750/109
⇒ P = $4750
Thus, the sum borrowed (P) = $4750 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 5177.5, then the Principal = 100/109 × 5177.5
= 100 × 5177.5/109
= 517750/109
= 4750
Thus, Principal = $4750
Thus, the sum borrowed = $4750 Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.
(3) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(4) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?
(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?
(6) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 2% simple interest?
(7) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 3 years.
(9) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.