Question:
How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?
Correct Answer
$7850
Solution And Explanation
Solution
Given,
Amount (A) = $8635
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
$8635 = P (1 + 2% × 5)
⇒ $8635 = P (1 + 2/100 × 5)
⇒ $8635 = P (1 + 2 × 5/100)
⇒ $8635 = P (1 + 10/100)
⇒ $8635 = P (100 + 10/100)
⇒ $8635 = P × 110/100
⇒ P × 110/100 = $8635
⇒ P = 8635/110/100
⇒ P = 8635 × 100/110
⇒ P = 8635 × 100/110
⇒ P = 863500/110
⇒ P = $7850
Thus, the sum borrowed (P) = $7850 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 8635, then the Principal = 100/110 × 8635
= 100 × 8635/110
= 863500/110
= 7850
Thus, Principal = $7850
Thus, the sum borrowed = $7850 Answer
Similar Questions
(1) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 7 years.
(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?
(4) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?
(5) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 3 years.
(6) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.
(7) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(8) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(9) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 2% simple interest?
(10) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.