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) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(2) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 7% simple interest?
(3) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?
(4) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?
(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.
(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.
(7) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 5% simple interest?
(8) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 4 years.
(9) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?
(10) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.