Question:
Jennifer had to pay $3542.5 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
$3250
Solution And Explanation
Solution
Given,
Amount (A) = $3542.5
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
$3542.5 = P (1 + 3% × 3)
⇒ $3542.5 = P (1 + 3/100 × 3)
⇒ $3542.5 = P (1 + 3 × 3/100)
⇒ $3542.5 = P (1 + 9/100)
⇒ $3542.5 = P (100 + 9/100)
⇒ $3542.5 = P × 109/100
⇒ P × 109/100 = $3542.5
⇒ P = 3542.5/109/100
⇒ P = 3542.5 × 100/109
⇒ P = 3542.5 × 100/109
⇒ P = 354250/109
⇒ P = $3250
Thus, the sum borrowed (P) = $3250 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 3542.5, then the Principal = 100/109 × 3542.5
= 100 × 3542.5/109
= 354250/109
= 3250
Thus, Principal = $3250
Thus, the sum borrowed = $3250 Answer
Similar Questions
(1) What amount does William have to pay after 5 years if he takes a loan of $3500 at 7% simple interest?
(2) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 3 years.
(4) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 7% simple interest?
(5) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 7% simple interest?
(6) If David paid $3808 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 10% simple interest?
(8) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.
(9) If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.