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) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(2) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 10% simple interest?
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.
(5) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
(6) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?
(7) Steven had to pay $5290 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 3 years.
(9) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.