Question:
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?
Correct Answer
$5250
Solution And Explanation
Solution
Given,
Amount (A) = $6037.5
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
$6037.5 = P (1 + 3% × 5)
⇒ $6037.5 = P (1 + 3/100 × 5)
⇒ $6037.5 = P (1 + 3 × 5/100)
⇒ $6037.5 = P (1 + 15/100)
⇒ $6037.5 = P (100 + 15/100)
⇒ $6037.5 = P × 115/100
⇒ P × 115/100 = $6037.5
⇒ P = 6037.5/115/100
⇒ P = 6037.5 × 100/115
⇒ P = 6037.5 × 100/115
⇒ P = 603750/115
⇒ P = $5250
Thus, the sum borrowed (P) = $5250 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 6037.5, then the Principal = 100/115 × 6037.5
= 100 × 6037.5/115
= 603750/115
= 5250
Thus, Principal = $5250
Thus, the sum borrowed = $5250 Answer
Similar Questions
(1) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 4 years.
(2) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?
(3) What amount does William have to pay after 5 years if he takes a loan of $3500 at 7% simple interest?
(4) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.
(5) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.
(7) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 2% simple interest?
(8) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6540 to clear it?
(9) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.
(10) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 7% simple interest?