Question:
How much loan did Michelle borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7992.5 to clear it?
Correct Answer
$6950
Solution And Explanation
Solution
Given,
Amount (A) = $7992.5
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
$7992.5 = P (1 + 3% × 5)
⇒ $7992.5 = P (1 + 3/100 × 5)
⇒ $7992.5 = P (1 + 3 × 5/100)
⇒ $7992.5 = P (1 + 15/100)
⇒ $7992.5 = P (100 + 15/100)
⇒ $7992.5 = P × 115/100
⇒ P × 115/100 = $7992.5
⇒ P = 7992.5/115/100
⇒ P = 7992.5 × 100/115
⇒ P = 7992.5 × 100/115
⇒ P = 799250/115
⇒ P = $6950
Thus, the sum borrowed (P) = $6950 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 7992.5, then the Principal = 100/115 × 7992.5
= 100 × 7992.5/115
= 799250/115
= 6950
Thus, Principal = $6950
Thus, the sum borrowed = $6950 Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.
(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.
(3) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8970 to clear it?
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.
(5) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?
(6) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.
(7) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.
(10) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.