Question:
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?
Correct Answer
$5500
Solution And Explanation
Solution
Given,
Amount (A) = $6875
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
$6875 = P (1 + 5% × 5)
⇒ $6875 = P (1 + 5/100 × 5)
⇒ $6875 = P (1 + 5 × 5/100)
⇒ $6875 = P (1 + 25/100)
⇒ $6875 = P (100 + 25/100)
⇒ $6875 = P × 125/100
⇒ P × 125/100 = $6875
⇒ P = 6875/125/100
⇒ P = 6875 × 100/125
⇒ P = 6875 × 100/125
⇒ P = 687500/125
⇒ P = $5500
Thus, the sum borrowed (P) = $5500 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 6875, then the Principal = 100/125 × 6875
= 100 × 6875/125
= 687500/125
= 5500
Thus, Principal = $5500
Thus, the sum borrowed = $5500 Answer
Similar Questions
(1) What amount does James have to pay after 6 years if he takes a loan of $3000 at 4% simple interest?
(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.
(4) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?
(6) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.
(8) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?
(9) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?
(10) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.