Question:
Emily had to pay $5035 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
$4750
Solution And Explanation
Solution
Given,
Amount (A) = $5035
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
$5035 = P (1 + 2% × 3)
⇒ $5035 = P (1 + 2/100 × 3)
⇒ $5035 = P (1 + 2 × 3/100)
⇒ $5035 = P (1 + 6/100)
⇒ $5035 = P (100 + 6/100)
⇒ $5035 = P × 106/100
⇒ P × 106/100 = $5035
⇒ P = 5035/106/100
⇒ P = 5035 × 100/106
⇒ P = 5035 × 100/106
⇒ P = 503500/106
⇒ P = $4750
Thus, the sum borrowed (P) = $4750 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 5035, then the Principal = 100/106 × 5035
= 100 × 5035/106
= 503500/106
= 4750
Thus, Principal = $4750
Thus, the sum borrowed = $4750 Answer
Similar Questions
(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 7 years.
(2) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 8 years.
(4) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(6) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9089 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.
(8) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?
(9) How much loan did Sharon borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9687.5 to clear it?
(10) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?