Question:
How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?
Correct Answer
$5100
Solution And Explanation
Solution
Given,
Amount (A) = $6375
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
$6375 = P (1 + 5% × 5)
⇒ $6375 = P (1 + 5/100 × 5)
⇒ $6375 = P (1 + 5 × 5/100)
⇒ $6375 = P (1 + 25/100)
⇒ $6375 = P (100 + 25/100)
⇒ $6375 = P × 125/100
⇒ P × 125/100 = $6375
⇒ P = 6375/125/100
⇒ P = 6375 × 100/125
⇒ P = 6375 × 100/125
⇒ P = 637500/125
⇒ P = $5100
Thus, the sum borrowed (P) = $5100 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 6375, then the Principal = 100/125 × 6375
= 100 × 6375/125
= 637500/125
= 5100
Thus, Principal = $5100
Thus, the sum borrowed = $5100 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
(2) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(3) William had to pay $3815 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 5% simple interest?
(5) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?
(6) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(8) If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.