Question:
How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?
Correct Answer
$5450
Solution And Explanation
Solution
Given,
Amount (A) = $5995
Rate of Simple Interest (R) = 2%
Time (T) = 5 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
$5995 = P (1 + 2% × 5)
⇒ $5995 = P (1 + 2/100 × 5)
⇒ $5995 = P (1 + 2 × 5/100)
⇒ $5995 = P (1 + 10/100)
⇒ $5995 = P (100 + 10/100)
⇒ $5995 = P × 110/100
⇒ P × 110/100 = $5995
⇒ P = 5995/110/100
⇒ P = 5995 × 100/110
⇒ P = 5995 × 100/110
⇒ P = 599500/110
⇒ P = $5450
Thus, the sum borrowed (P) = $5450 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 = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 5995, then the Principal = 100/110 × 5995
= 100 × 5995/110
= 599500/110
= 5450
Thus, Principal = $5450
Thus, the sum borrowed = $5450 Answer
Similar Questions
(1) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 8% simple interest?
(2) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(3) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(4) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(5) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?
(6) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 3 years.
(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?
(9) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.
(10) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6888 to clear the loan, then find the time period of the loan.