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 8% simple interest?
(2) What amount will be due after 2 years if William borrowed a sum of $3250 at a 7% simple interest?
(3) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 4% simple interest?
(5) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
(7) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(8) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 8 years.
(10) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.