Question:
How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?
Correct Answer
$6500
Solution And Explanation
Solution
Given,
Amount (A) = $8125
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
$8125 = P (1 + 5% × 5)
⇒ $8125 = P (1 + 5/100 × 5)
⇒ $8125 = P (1 + 5 × 5/100)
⇒ $8125 = P (1 + 25/100)
⇒ $8125 = P (100 + 25/100)
⇒ $8125 = P × 125/100
⇒ P × 125/100 = $8125
⇒ P = 8125/125/100
⇒ P = 8125 × 100/125
⇒ P = 8125 × 100/125
⇒ P = 812500/125
⇒ P = $6500
Thus, the sum borrowed (P) = $6500 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 8125, then the Principal = 100/125 × 8125
= 100 × 8125/125
= 812500/125
= 6500
Thus, Principal = $6500
Thus, the sum borrowed = $6500 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(3) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?
(4) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 4 years.
(5) How much loan did Lisa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6957.5 to clear it?
(6) Kimberly had to pay $5347.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 7 years.
(8) In how much time a principal of $3000 will amount to $3300 at a simple interest of 5% per annum?
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 3 years.
(10) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.