Question:
How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?
Correct Answer
$8000
Solution And Explanation
Solution
Given,
Amount (A) = $10000
Rate of Simple Interest (R) = 5%
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
$10000 = P (1 + 5% × 5)
⇒ $10000 = P (1 + 5/100 × 5)
⇒ $10000 = P (1 + 5 × 5/100)
⇒ $10000 = P (1 + 25/100)
⇒ $10000 = P (100 + 25/100)
⇒ $10000 = P × 125/100
⇒ P × 125/100 = $10000
⇒ P = 10000/125/100
⇒ P = 10000 × 100/125
⇒ P = 10000 × 100/125
⇒ P = 1000000/125
⇒ P = $8000
Thus, the sum borrowed (P) = $8000 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 = 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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 10000, then the Principal = 100/125 × 10000
= 100 × 10000/125
= 1000000/125
= 8000
Thus, Principal = $8000
Thus, the sum borrowed = $8000 Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 8 years.
(3) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 7 years.
(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 3 years.
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.
(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 4 years.
(9) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.
(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.