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) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(2) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?
(3) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?
(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.
(5) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
(6) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 8 years.
(8) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(10) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.