Question:
Jessica had to pay $4312.5 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
$3750
Solution And Explanation
Solution
Given,
Amount (A) = $4312.5
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
$4312.5 = P (1 + 5% × 3)
⇒ $4312.5 = P (1 + 5/100 × 3)
⇒ $4312.5 = P (1 + 5 × 3/100)
⇒ $4312.5 = P (1 + 15/100)
⇒ $4312.5 = P (100 + 15/100)
⇒ $4312.5 = P × 115/100
⇒ P × 115/100 = $4312.5
⇒ P = 4312.5/115/100
⇒ P = 4312.5 × 100/115
⇒ P = 4312.5 × 100/115
⇒ P = 431250/115
⇒ P = $3750
Thus, the sum borrowed (P) = $3750 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 4312.5, then the Principal = 100/115 × 4312.5
= 100 × 4312.5/115
= 431250/115
= 3750
Thus, Principal = $3750
Thus, the sum borrowed = $3750 Answer
Similar Questions
(1) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 5% simple interest?
(2) If Jessica paid $4050 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 3 years.
(5) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(7) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(8) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.
(10) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.