Question:
How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?
Correct Answer
$7650
Solution And Explanation
Solution
Given,
Amount (A) = $8415
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
$8415 = P (1 + 2% × 5)
⇒ $8415 = P (1 + 2/100 × 5)
⇒ $8415 = P (1 + 2 × 5/100)
⇒ $8415 = P (1 + 10/100)
⇒ $8415 = P (100 + 10/100)
⇒ $8415 = P × 110/100
⇒ P × 110/100 = $8415
⇒ P = 8415/110/100
⇒ P = 8415 × 100/110
⇒ P = 8415 × 100/110
⇒ P = 841500/110
⇒ P = $7650
Thus, the sum borrowed (P) = $7650 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 8415, then the Principal = 100/110 × 8415
= 100 × 8415/110
= 841500/110
= 7650
Thus, Principal = $7650
Thus, the sum borrowed = $7650 Answer
Similar Questions
(1) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.
(3) 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?
(4) Patricia had to pay $3433.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(6) If Susan borrowed $3650 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) Ashley had to pay $5096 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.
(10) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?