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 James have to pay after 5 years if he takes a loan of $3000 at 9% simple interest?
(2) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?
(3) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(4) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?
(6) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9536 to clear the loan, then find the time period of the loan.
(7) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 7 years.
(9) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 2% simple interest.