Question:
How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?
Correct Answer
$5650
Solution And Explanation
Solution
Given,
Amount (A) = $6497.5
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
$6497.5 = P (1 + 3% × 5)
⇒ $6497.5 = P (1 + 3/100 × 5)
⇒ $6497.5 = P (1 + 3 × 5/100)
⇒ $6497.5 = P (1 + 15/100)
⇒ $6497.5 = P (100 + 15/100)
⇒ $6497.5 = P × 115/100
⇒ P × 115/100 = $6497.5
⇒ P = 6497.5/115/100
⇒ P = 6497.5 × 100/115
⇒ P = 6497.5 × 100/115
⇒ P = 649750/115
⇒ P = $5650
Thus, the sum borrowed (P) = $5650 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 6497.5, then the Principal = 100/115 × 6497.5
= 100 × 6497.5/115
= 649750/115
= 5650
Thus, Principal = $5650
Thus, the sum borrowed = $5650 Answer
Similar Questions
(1) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(2) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9112 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 3 years.
(5) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(6) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(7) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 6% simple interest?
(8) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 8 years.
(9) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?
(10) How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?