Question:
Elizabeth had to pay $3657 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
$3450
Solution And Explanation
Solution
Given,
Amount (A) = $3657
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
$3657 = P (1 + 2% × 3)
⇒ $3657 = P (1 + 2/100 × 3)
⇒ $3657 = P (1 + 2 × 3/100)
⇒ $3657 = P (1 + 6/100)
⇒ $3657 = P (100 + 6/100)
⇒ $3657 = P × 106/100
⇒ P × 106/100 = $3657
⇒ P = 3657/106/100
⇒ P = 3657 × 100/106
⇒ P = 3657 × 100/106
⇒ P = 365700/106
⇒ P = $3450
Thus, the sum borrowed (P) = $3450 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 3657, then the Principal = 100/106 × 3657
= 100 × 3657/106
= 365700/106
= 3450
Thus, Principal = $3450
Thus, the sum borrowed = $3450 Answer
Similar Questions
(1) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?
(2) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?
(4) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.
(5) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?
(6) How much loan did Lisa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7260 to clear it?
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.
(8) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.
(10) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.