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 does John have to pay after 5 years if he takes a loan of $3200 at 6% simple interest?
(2) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?
(3) How much loan did Timothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8880 to clear it?
(4) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(5) If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 7 years.
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 3 years.
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 7 years.
(10) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?