Question:
How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?
Correct Answer
$5150
Solution And Explanation
Solution
Given,
Amount (A) = $5665
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
$5665 = P (1 + 2% × 5)
⇒ $5665 = P (1 + 2/100 × 5)
⇒ $5665 = P (1 + 2 × 5/100)
⇒ $5665 = P (1 + 10/100)
⇒ $5665 = P (100 + 10/100)
⇒ $5665 = P × 110/100
⇒ P × 110/100 = $5665
⇒ P = 5665/110/100
⇒ P = 5665 × 100/110
⇒ P = 5665 × 100/110
⇒ P = 566500/110
⇒ P = $5150
Thus, the sum borrowed (P) = $5150 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 5665, then the Principal = 100/110 × 5665
= 100 × 5665/110
= 566500/110
= 5150
Thus, Principal = $5150
Thus, the sum borrowed = $5150 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(2) Thomas had to pay $4370 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.
(4) If Michael borrowed $3300 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 8 years.
(6) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?
(8) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?
(9) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 9% simple interest?
(10) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.