Question:
How much loan did Ashley borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7532.5 to clear it?
Correct Answer
$6550
Solution And Explanation
Solution
Given,
Amount (A) = $7532.5
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
$7532.5 = P (1 + 3% × 5)
⇒ $7532.5 = P (1 + 3/100 × 5)
⇒ $7532.5 = P (1 + 3 × 5/100)
⇒ $7532.5 = P (1 + 15/100)
⇒ $7532.5 = P (100 + 15/100)
⇒ $7532.5 = P × 115/100
⇒ P × 115/100 = $7532.5
⇒ P = 7532.5/115/100
⇒ P = 7532.5 × 100/115
⇒ P = 7532.5 × 100/115
⇒ P = 753250/115
⇒ P = $6550
Thus, the sum borrowed (P) = $6550 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 7532.5, then the Principal = 100/115 × 7532.5
= 100 × 7532.5/115
= 753250/115
= 6550
Thus, Principal = $6550
Thus, the sum borrowed = $6550 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.
(2) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?
(3) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(4) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.
(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 9% simple interest?
(7) How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?
(8) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 to clear the loan, then find the time period of the loan.
(9) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6037.5 to clear it?
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.