Question:
How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?
Correct Answer
$5250
Solution And Explanation
Solution
Given,
Amount (A) = $5775
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
$5775 = P (1 + 2% × 5)
⇒ $5775 = P (1 + 2/100 × 5)
⇒ $5775 = P (1 + 2 × 5/100)
⇒ $5775 = P (1 + 10/100)
⇒ $5775 = P (100 + 10/100)
⇒ $5775 = P × 110/100
⇒ P × 110/100 = $5775
⇒ P = 5775/110/100
⇒ P = 5775 × 100/110
⇒ P = 5775 × 100/110
⇒ P = 577500/110
⇒ P = $5250
Thus, the sum borrowed (P) = $5250 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 5775, then the Principal = 100/110 × 5775
= 100 × 5775/110
= 577500/110
= 5250
Thus, Principal = $5250
Thus, the sum borrowed = $5250 Answer
Similar Questions
(1) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 7 years.
(2) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.
(4) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
(5) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(6) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.
(9) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(10) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 3 years.