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 William borrowed a sum of $3500 at 3% simple interest for 3 years.
(2) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 7 years.
(4) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.
(6) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 3 years.
(8) Joseph had to pay $4033 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 3% simple interest?
(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?