Question:
Linda had to pay $3551 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
$3350
Solution And Explanation
Solution
Given,
Amount (A) = $3551
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
$3551 = P (1 + 2% × 3)
⇒ $3551 = P (1 + 2/100 × 3)
⇒ $3551 = P (1 + 2 × 3/100)
⇒ $3551 = P (1 + 6/100)
⇒ $3551 = P (100 + 6/100)
⇒ $3551 = P × 106/100
⇒ P × 106/100 = $3551
⇒ P = 3551/106/100
⇒ P = 3551 × 100/106
⇒ P = 3551 × 100/106
⇒ P = 355100/106
⇒ P = $3350
Thus, the sum borrowed (P) = $3350 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 3551, then the Principal = 100/106 × 3551
= 100 × 3551/106
= 355100/106
= 3350
Thus, Principal = $3350
Thus, the sum borrowed = $3350 Answer
Similar Questions
(1) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?
(2) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 7% simple interest?
(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(5) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 6% simple interest?
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 4 years.
(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?
(9) How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?
(10) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.