Question:
How much loan did Margaret borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7937.5 to clear it?
Correct Answer
$6350
Solution And Explanation
Solution
Given,
Amount (A) = $7937.5
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
$7937.5 = P (1 + 5% × 5)
⇒ $7937.5 = P (1 + 5/100 × 5)
⇒ $7937.5 = P (1 + 5 × 5/100)
⇒ $7937.5 = P (1 + 25/100)
⇒ $7937.5 = P (100 + 25/100)
⇒ $7937.5 = P × 125/100
⇒ P × 125/100 = $7937.5
⇒ P = 7937.5/125/100
⇒ P = 7937.5 × 100/125
⇒ P = 7937.5 × 100/125
⇒ P = 793750/125
⇒ P = $6350
Thus, the sum borrowed (P) = $6350 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 7937.5, then the Principal = 100/125 × 7937.5
= 100 × 7937.5/125
= 793750/125
= 6350
Thus, Principal = $6350
Thus, the sum borrowed = $6350 Answer
Similar Questions
(1) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 9% simple interest?
(3) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?
(5) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(6) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) In how much time a principal of $3200 will amount to $3584 at a simple interest of 4% per annum?
(8) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 4 years.
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 4 years.
(10) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.