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 10 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.
(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 2% simple interest?
(3) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 7 years.
(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 7% simple interest?
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.
(7) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.
(8) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?
(9) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(10) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.