Question:
How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?
Correct Answer
$7950
Solution And Explanation
Solution
Given,
Amount (A) = $9937.5
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
$9937.5 = P (1 + 5% × 5)
⇒ $9937.5 = P (1 + 5/100 × 5)
⇒ $9937.5 = P (1 + 5 × 5/100)
⇒ $9937.5 = P (1 + 25/100)
⇒ $9937.5 = P (100 + 25/100)
⇒ $9937.5 = P × 125/100
⇒ P × 125/100 = $9937.5
⇒ P = 9937.5/125/100
⇒ P = 9937.5 × 100/125
⇒ P = 9937.5 × 100/125
⇒ P = 993750/125
⇒ P = $7950
Thus, the sum borrowed (P) = $7950 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 9937.5, then the Principal = 100/125 × 9937.5
= 100 × 9937.5/125
= 993750/125
= 7950
Thus, Principal = $7950
Thus, the sum borrowed = $7950 Answer
Similar Questions
(1) Ashley had to pay $5232.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 7 years.
(3) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 4 years.
(4) If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?
(6) If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.
(9) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 8 years.