Question:
How much loan did Lisa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6655 to clear it?
Correct Answer
$6050
Solution And Explanation
Solution
Given,
Amount (A) = $6655
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
$6655 = P (1 + 2% × 5)
⇒ $6655 = P (1 + 2/100 × 5)
⇒ $6655 = P (1 + 2 × 5/100)
⇒ $6655 = P (1 + 10/100)
⇒ $6655 = P (100 + 10/100)
⇒ $6655 = P × 110/100
⇒ P × 110/100 = $6655
⇒ P = 6655/110/100
⇒ P = 6655 × 100/110
⇒ P = 6655 × 100/110
⇒ P = 665500/110
⇒ P = $6050
Thus, the sum borrowed (P) = $6050 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 6655, then the Principal = 100/110 × 6655
= 100 × 6655/110
= 665500/110
= 6050
Thus, Principal = $6050
Thus, the sum borrowed = $6050 Answer
Similar Questions
(1) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.
(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 10% simple interest?
(3) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.
(4) How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?
(5) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 4% simple interest?
(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.
(8) What amount will be due after 2 years if James borrowed a sum of $3000 at a 7% simple interest?
(9) What amount does John have to pay after 5 years if he takes a loan of $3200 at 10% simple interest?
(10) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.