Question:
How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?
Correct Answer
$5000
Solution And Explanation
Solution
Given,
Amount (A) = $6250
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
$6250 = P (1 + 5% × 5)
⇒ $6250 = P (1 + 5/100 × 5)
⇒ $6250 = P (1 + 5 × 5/100)
⇒ $6250 = P (1 + 25/100)
⇒ $6250 = P (100 + 25/100)
⇒ $6250 = P × 125/100
⇒ P × 125/100 = $6250
⇒ P = 6250/125/100
⇒ P = 6250 × 100/125
⇒ P = 6250 × 100/125
⇒ P = 625000/125
⇒ P = $5000
Thus, the sum borrowed (P) = $5000 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 6250, then the Principal = 100/125 × 6250
= 100 × 6250/125
= 625000/125
= 5000
Thus, Principal = $5000
Thus, the sum borrowed = $5000 Answer
Similar Questions
(1) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.
(2) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
(4) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?
(5) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
(6) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.
(7) How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?
(8) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?
(9) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?
(10) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?