Question:
How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?
Correct Answer
$5700
Solution And Explanation
Solution
Given,
Amount (A) = $7125
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
$7125 = P (1 + 5% × 5)
⇒ $7125 = P (1 + 5/100 × 5)
⇒ $7125 = P (1 + 5 × 5/100)
⇒ $7125 = P (1 + 25/100)
⇒ $7125 = P (100 + 25/100)
⇒ $7125 = P × 125/100
⇒ P × 125/100 = $7125
⇒ P = 7125/125/100
⇒ P = 7125 × 100/125
⇒ P = 7125 × 100/125
⇒ P = 712500/125
⇒ P = $5700
Thus, the sum borrowed (P) = $5700 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 7125, then the Principal = 100/125 × 7125
= 100 × 7125/125
= 712500/125
= 5700
Thus, Principal = $5700
Thus, the sum borrowed = $5700 Answer
Similar Questions
(1) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 6% simple interest?
(2) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?
(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.
(4) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?
(5) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 3 years.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.
(8) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.
(9) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?
(10) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?