Question:
How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?
Correct Answer
$5300
Solution And Explanation
Solution
Given,
Amount (A) = $6625
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
$6625 = P (1 + 5% × 5)
⇒ $6625 = P (1 + 5/100 × 5)
⇒ $6625 = P (1 + 5 × 5/100)
⇒ $6625 = P (1 + 25/100)
⇒ $6625 = P (100 + 25/100)
⇒ $6625 = P × 125/100
⇒ P × 125/100 = $6625
⇒ P = 6625/125/100
⇒ P = 6625 × 100/125
⇒ P = 6625 × 100/125
⇒ P = 662500/125
⇒ P = $5300
Thus, the sum borrowed (P) = $5300 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 6625, then the Principal = 100/125 × 6625
= 100 × 6625/125
= 662500/125
= 5300
Thus, Principal = $5300
Thus, the sum borrowed = $5300 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(2) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.
(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.
(5) What amount will be due after 2 years if William borrowed a sum of $3250 at a 5% simple interest?
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 7 years.
(7) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 8% simple interest?
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?
(9) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 4 years.
(10) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8296 to clear the loan, then find the time period of the loan.