Question:
Susan had to pay $3869 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
$3650
Solution And Explanation
Solution
Given,
Amount (A) = $3869
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
$3869 = P (1 + 2% × 3)
⇒ $3869 = P (1 + 2/100 × 3)
⇒ $3869 = P (1 + 2 × 3/100)
⇒ $3869 = P (1 + 6/100)
⇒ $3869 = P (100 + 6/100)
⇒ $3869 = P × 106/100
⇒ P × 106/100 = $3869
⇒ P = 3869/106/100
⇒ P = 3869 × 100/106
⇒ P = 3869 × 100/106
⇒ P = 386900/106
⇒ P = $3650
Thus, the sum borrowed (P) = $3650 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 3869, then the Principal = 100/106 × 3869
= 100 × 3869/106
= 386900/106
= 3650
Thus, Principal = $3650
Thus, the sum borrowed = $3650 Answer
Similar Questions
(1) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(2) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.
(4) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.
(5) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?
(6) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.
(7) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?
(8) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 5% simple interest?
(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 7 years.
(10) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.