Question:
How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?
Correct Answer
$7950
Solution And Explanation
Solution
Given,
Amount (A) = $9142.5
Rate of Simple Interest (R) = 3%
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
$9142.5 = P (1 + 3% × 5)
⇒ $9142.5 = P (1 + 3/100 × 5)
⇒ $9142.5 = P (1 + 3 × 5/100)
⇒ $9142.5 = P (1 + 15/100)
⇒ $9142.5 = P (100 + 15/100)
⇒ $9142.5 = P × 115/100
⇒ P × 115/100 = $9142.5
⇒ P = 9142.5/115/100
⇒ P = 9142.5 × 100/115
⇒ P = 9142.5 × 100/115
⇒ P = 914250/115
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 9142.5, then the Principal = 100/115 × 9142.5
= 100 × 9142.5/115
= 914250/115
= 7950
Thus, Principal = $7950
Thus, the sum borrowed = $7950 Answer
Similar Questions
(1) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.
(3) Donna had to pay $5286.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 4% simple interest?
(5) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(6) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 8 years.
(7) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(8) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.
(10) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.