Question:
How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?
Correct Answer
$7550
Solution And Explanation
Solution
Given,
Amount (A) = $8682.5
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
$8682.5 = P (1 + 3% × 5)
⇒ $8682.5 = P (1 + 3/100 × 5)
⇒ $8682.5 = P (1 + 3 × 5/100)
⇒ $8682.5 = P (1 + 15/100)
⇒ $8682.5 = P (100 + 15/100)
⇒ $8682.5 = P × 115/100
⇒ P × 115/100 = $8682.5
⇒ P = 8682.5/115/100
⇒ P = 8682.5 × 100/115
⇒ P = 8682.5 × 100/115
⇒ P = 868250/115
⇒ 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 = 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 8682.5, then the Principal = 100/115 × 8682.5
= 100 × 8682.5/115
= 868250/115
= 7550
Thus, Principal = $7550
Thus, the sum borrowed = $7550 Answer
Similar Questions
(1) How much loan did Michelle borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8340 to clear it?
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 7 years.
(3) What amount does David have to pay after 6 years if he takes a loan of $3400 at 10% simple interest?
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.
(5) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 10% simple interest?
(6) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.
(7) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 3 years.
(9) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?