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) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?
(2) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 6% simple interest?
(3) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(5) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 8 years.
(7) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?
(9) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.
(10) If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.