Question:
Joshua had to pay $5635 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
$4900
Solution And Explanation
Solution
Given,
Amount (A) = $5635
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
$5635 = P (1 + 5% × 3)
⇒ $5635 = P (1 + 5/100 × 3)
⇒ $5635 = P (1 + 5 × 3/100)
⇒ $5635 = P (1 + 15/100)
⇒ $5635 = P (100 + 15/100)
⇒ $5635 = P × 115/100
⇒ P × 115/100 = $5635
⇒ P = 5635/115/100
⇒ P = 5635 × 100/115
⇒ P = 5635 × 100/115
⇒ P = 563500/115
⇒ P = $4900
Thus, the sum borrowed (P) = $4900 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 5635, then the Principal = 100/115 × 5635
= 100 × 5635/115
= 563500/115
= 4900
Thus, Principal = $4900
Thus, the sum borrowed = $4900 Answer
Similar Questions
(1) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?
(2) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.
(3) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.
(4) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.
(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(7) What amount will be due after 2 years if John borrowed a sum of $3100 at a 4% simple interest?
(8) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?
(9) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.
(10) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 10% simple interest.