Question:
Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
Correct Answer
$4050
Solution And Explanation
Solution
Given,
Amount (A) = $4657.5
Rate of Simple Interest (R) = 5%
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
$4657.5 = P (1 + 5% × 3)
⇒ $4657.5 = P (1 + 5/100 × 3)
⇒ $4657.5 = P (1 + 5 × 3/100)
⇒ $4657.5 = P (1 + 15/100)
⇒ $4657.5 = P (100 + 15/100)
⇒ $4657.5 = P × 115/100
⇒ P × 115/100 = $4657.5
⇒ P = 4657.5/115/100
⇒ P = 4657.5 × 100/115
⇒ P = 4657.5 × 100/115
⇒ P = 465750/115
⇒ P = $4050
Thus, the sum borrowed (P) = $4050 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 15
Thus, simple interest for 3 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 4657.5, then the Principal = 100/115 × 4657.5
= 100 × 4657.5/115
= 465750/115
= 4050
Thus, Principal = $4050
Thus, the sum borrowed = $4050 Answer
Similar Questions
(1) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 10% simple interest?
(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.
(4) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(5) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?
(7) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.
(8) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.
(10) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.