Question:
How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?
Correct Answer
$6950
Solution And Explanation
Solution
Given,
Amount (A) = $7645
Rate of Simple Interest (R) = 2%
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
$7645 = P (1 + 2% × 5)
⇒ $7645 = P (1 + 2/100 × 5)
⇒ $7645 = P (1 + 2 × 5/100)
⇒ $7645 = P (1 + 10/100)
⇒ $7645 = P (100 + 10/100)
⇒ $7645 = P × 110/100
⇒ P × 110/100 = $7645
⇒ P = 7645/110/100
⇒ P = 7645 × 100/110
⇒ P = 7645 × 100/110
⇒ P = 764500/110
⇒ 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 7645, then the Principal = 100/110 × 7645
= 100 × 7645/110
= 764500/110
= 6950
Thus, Principal = $6950
Thus, the sum borrowed = $6950 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
(2) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.
(3) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 4 years.
(5) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(7) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(8) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(9) How much loan did Jessica borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7187.5 to clear it?
(10) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.