Question:
How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?
Correct Answer
$7950
Solution And Explanation
Solution
Given,
Amount (A) = $9540
Rate of Simple Interest (R) = 4%
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
$9540 = P (1 + 4% × 5)
⇒ $9540 = P (1 + 4/100 × 5)
⇒ $9540 = P (1 + 4 × 5/100)
⇒ $9540 = P (1 + 20/100)
⇒ $9540 = P (100 + 20/100)
⇒ $9540 = P × 120/100
⇒ P × 120/100 = $9540
⇒ P = 9540/120/100
⇒ P = 9540 × 100/120
⇒ P = 9540 × 100/120
⇒ P = 954000/120
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 9540, then the Principal = 100/120 × 9540
= 100 × 9540/120
= 954000/120
= 7950
Thus, Principal = $7950
Thus, the sum borrowed = $7950 Answer
Similar Questions
(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.
(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 8% simple interest?
(3) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?
(4) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $7752 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.
(6) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 4 years.
(7) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
(8) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 3 years.
(9) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.
(10) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?