Question:
How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?
Correct Answer
$5200
Solution And Explanation
Solution
Given,
Amount (A) = $6500
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
$6500 = P (1 + 5% × 5)
⇒ $6500 = P (1 + 5/100 × 5)
⇒ $6500 = P (1 + 5 × 5/100)
⇒ $6500 = P (1 + 25/100)
⇒ $6500 = P (100 + 25/100)
⇒ $6500 = P × 125/100
⇒ P × 125/100 = $6500
⇒ P = 6500/125/100
⇒ P = 6500 × 100/125
⇒ P = 6500 × 100/125
⇒ P = 650000/125
⇒ P = $5200
Thus, the sum borrowed (P) = $5200 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 6500, then the Principal = 100/125 × 6500
= 100 × 6500/125
= 650000/125
= 5200
Thus, Principal = $5200
Thus, the sum borrowed = $5200 Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.
(2) What amount will be due after 2 years if David borrowed a sum of $3200 at a 4% simple interest?
(3) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.
(4) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?
(5) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(6) Betty had to pay $4887.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(8) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?
(9) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(10) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?