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) In how much time a principal of $3150 will amount to $3528 at a simple interest of 3% per annum?
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 4 years.
(3) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(4) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(5) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.
(6) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?
(7) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 4% simple interest?
(8) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
(9) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.
(10) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.