Question:
How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?
Correct Answer
$7150
Solution And Explanation
Solution
Given,
Amount (A) = $8937.5
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
$8937.5 = P (1 + 5% × 5)
⇒ $8937.5 = P (1 + 5/100 × 5)
⇒ $8937.5 = P (1 + 5 × 5/100)
⇒ $8937.5 = P (1 + 25/100)
⇒ $8937.5 = P (100 + 25/100)
⇒ $8937.5 = P × 125/100
⇒ P × 125/100 = $8937.5
⇒ P = 8937.5/125/100
⇒ P = 8937.5 × 100/125
⇒ P = 8937.5 × 100/125
⇒ P = 893750/125
⇒ P = $7150
Thus, the sum borrowed (P) = $7150 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 8937.5, then the Principal = 100/125 × 8937.5
= 100 × 8937.5/125
= 893750/125
= 7150
Thus, Principal = $7150
Thus, the sum borrowed = $7150 Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.
(2) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.
(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?
(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(6) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?
(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?
(8) Karen had to pay $4305.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 7% simple interest?
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.