Question:
Robert had to pay $3379 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
$3100
Solution And Explanation
Solution
Given,
Amount (A) = $3379
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
$3379 = P (1 + 3% × 3)
⇒ $3379 = P (1 + 3/100 × 3)
⇒ $3379 = P (1 + 3 × 3/100)
⇒ $3379 = P (1 + 9/100)
⇒ $3379 = P (100 + 9/100)
⇒ $3379 = P × 109/100
⇒ P × 109/100 = $3379
⇒ P = 3379/109/100
⇒ P = 3379 × 100/109
⇒ P = 3379 × 100/109
⇒ P = 337900/109
⇒ P = $3100
Thus, the sum borrowed (P) = $3100 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 3379, then the Principal = 100/109 × 3379
= 100 × 3379/109
= 337900/109
= 3100
Thus, Principal = $3100
Thus, the sum borrowed = $3100 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(2) How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?
(3) How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?
(4) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.
(6) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?
(7) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.
(9) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?
(10) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 3 years.