Question:
How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?
Correct Answer
$6400
Solution And Explanation
Solution
Given,
Amount (A) = $8000
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
$8000 = P (1 + 5% × 5)
⇒ $8000 = P (1 + 5/100 × 5)
⇒ $8000 = P (1 + 5 × 5/100)
⇒ $8000 = P (1 + 25/100)
⇒ $8000 = P (100 + 25/100)
⇒ $8000 = P × 125/100
⇒ P × 125/100 = $8000
⇒ P = 8000/125/100
⇒ P = 8000 × 100/125
⇒ P = 8000 × 100/125
⇒ P = 800000/125
⇒ P = $6400
Thus, the sum borrowed (P) = $6400 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 8000, then the Principal = 100/125 × 8000
= 100 × 8000/125
= 800000/125
= 6400
Thus, Principal = $6400
Thus, the sum borrowed = $6400 Answer
Similar Questions
(1) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?
(2) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?
(4) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
(5) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?
(6) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.
(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.
(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.
(10) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 10% simple interest?