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) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.
(3) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?
(4) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(5) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
(6) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.
(8) If Donna paid $5432 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 4 years.
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 8 years.