Question:
How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?
Correct Answer
$7550
Solution And Explanation
Solution
Given,
Amount (A) = $9437.5
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
$9437.5 = P (1 + 5% × 5)
⇒ $9437.5 = P (1 + 5/100 × 5)
⇒ $9437.5 = P (1 + 5 × 5/100)
⇒ $9437.5 = P (1 + 25/100)
⇒ $9437.5 = P (100 + 25/100)
⇒ $9437.5 = P × 125/100
⇒ P × 125/100 = $9437.5
⇒ P = 9437.5/125/100
⇒ P = 9437.5 × 100/125
⇒ P = 9437.5 × 100/125
⇒ P = 943750/125
⇒ P = $7550
Thus, the sum borrowed (P) = $7550 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 9437.5, then the Principal = 100/125 × 9437.5
= 100 × 9437.5/125
= 943750/125
= 7550
Thus, Principal = $7550
Thus, the sum borrowed = $7550 Answer
Similar Questions
(1) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 4 years.
(2) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(3) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.
(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?
(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 7 years.
(6) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 4 years.
(7) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
(8) 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?
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 8 years.
(10) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.