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 Karen borrowed a sum of $5950 at 4% simple interest for 7 years.
(2) If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.
(4) How much loan did Emily borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8437.5 to clear it?
(5) How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?
(6) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 3 years.
(8) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.
(9) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 8% simple interest?
(10) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.