Question:
How much loan did Lisa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6957.5 to clear it?
Correct Answer
$6050
Solution And Explanation
Solution
Given,
Amount (A) = $6957.5
Rate of Simple Interest (R) = 3%
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
$6957.5 = P (1 + 3% × 5)
⇒ $6957.5 = P (1 + 3/100 × 5)
⇒ $6957.5 = P (1 + 3 × 5/100)
⇒ $6957.5 = P (1 + 15/100)
⇒ $6957.5 = P (100 + 15/100)
⇒ $6957.5 = P × 115/100
⇒ P × 115/100 = $6957.5
⇒ P = 6957.5/115/100
⇒ P = 6957.5 × 100/115
⇒ P = 6957.5 × 100/115
⇒ P = 695750/115
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 6957.5, then the Principal = 100/115 × 6957.5
= 100 × 6957.5/115
= 695750/115
= 6050
Thus, Principal = $6050
Thus, the sum borrowed = $6050 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 4 years.
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.
(5) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(6) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?
(7) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7748 to clear the loan, then find the time period of the loan.
(8) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(10) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.