Question:
How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?
Correct Answer
$6400
Solution And Explanation
Solution
Given,
Amount (A) = $7360
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
$7360 = P (1 + 3% × 5)
⇒ $7360 = P (1 + 3/100 × 5)
⇒ $7360 = P (1 + 3 × 5/100)
⇒ $7360 = P (1 + 15/100)
⇒ $7360 = P (100 + 15/100)
⇒ $7360 = P × 115/100
⇒ P × 115/100 = $7360
⇒ P = 7360/115/100
⇒ P = 7360 × 100/115
⇒ P = 7360 × 100/115
⇒ P = 736000/115
⇒ P = $6400
Thus, the sum borrowed (P) = $6400 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 7360, then the Principal = 100/115 × 7360
= 100 × 7360/115
= 736000/115
= 6400
Thus, Principal = $6400
Thus, the sum borrowed = $6400 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.
(2) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?
(3) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.
(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?
(5) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 2% simple interest?
(6) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 5% simple interest.
(7) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 6% simple interest?
(8) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(9) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?
(10) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.