Question:
How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?
Correct Answer
$7750
Solution And Explanation
Solution
Given,
Amount (A) = $9300
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
$9300 = P (1 + 4% × 5)
⇒ $9300 = P (1 + 4/100 × 5)
⇒ $9300 = P (1 + 4 × 5/100)
⇒ $9300 = P (1 + 20/100)
⇒ $9300 = P (100 + 20/100)
⇒ $9300 = P × 120/100
⇒ P × 120/100 = $9300
⇒ P = 9300/120/100
⇒ P = 9300 × 100/120
⇒ P = 9300 × 100/120
⇒ P = 930000/120
⇒ P = $7750
Thus, the sum borrowed (P) = $7750 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 9300, then the Principal = 100/120 × 9300
= 100 × 9300/120
= 930000/120
= 7750
Thus, Principal = $7750
Thus, the sum borrowed = $7750 Answer
Similar Questions
(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 7 years.
(2) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8195 to clear the loan, then find the time period of the loan.
(3) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 4 years.
(5) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.
(7) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?
(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?
(10) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.