Question:
How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?
Correct Answer
$6000
Solution And Explanation
Solution
Given,
Amount (A) = $7500
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
$7500 = P (1 + 5% × 5)
⇒ $7500 = P (1 + 5/100 × 5)
⇒ $7500 = P (1 + 5 × 5/100)
⇒ $7500 = P (1 + 25/100)
⇒ $7500 = P (100 + 25/100)
⇒ $7500 = P × 125/100
⇒ P × 125/100 = $7500
⇒ P = 7500/125/100
⇒ P = 7500 × 100/125
⇒ P = 7500 × 100/125
⇒ P = 750000/125
⇒ P = $6000
Thus, the sum borrowed (P) = $6000 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 7500, then the Principal = 100/125 × 7500
= 100 × 7500/125
= 750000/125
= 6000
Thus, Principal = $6000
Thus, the sum borrowed = $6000 Answer
Similar Questions
(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.
(2) How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 8 years.
(4) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?
(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?
(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 3 years.
(7) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(8) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 5% simple interest?
(9) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?
(10) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.