Question:
How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?
Correct Answer
$7450
Solution And Explanation
Solution
Given,
Amount (A) = $8195
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
$8195 = P (1 + 2% × 5)
⇒ $8195 = P (1 + 2/100 × 5)
⇒ $8195 = P (1 + 2 × 5/100)
⇒ $8195 = P (1 + 10/100)
⇒ $8195 = P (100 + 10/100)
⇒ $8195 = P × 110/100
⇒ P × 110/100 = $8195
⇒ P = 8195/110/100
⇒ P = 8195 × 100/110
⇒ P = 8195 × 100/110
⇒ P = 819500/110
⇒ P = $7450
Thus, the sum borrowed (P) = $7450 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 8195, then the Principal = 100/110 × 8195
= 100 × 8195/110
= 819500/110
= 7450
Thus, Principal = $7450
Thus, the sum borrowed = $7450 Answer
Similar Questions
(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.
(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 7 years.
(3) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?
(4) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 3 years.
(5) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 7% simple interest.
(6) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.
(7) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?
(8) Donald had to pay $4770 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 4 years.