Question:
How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?
Correct Answer
$5250
Solution And Explanation
Solution
Given,
Amount (A) = $6300
Rate of Simple Interest (R) = 4%
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
$6300 = P (1 + 4% × 5)
⇒ $6300 = P (1 + 4/100 × 5)
⇒ $6300 = P (1 + 4 × 5/100)
⇒ $6300 = P (1 + 20/100)
⇒ $6300 = P (100 + 20/100)
⇒ $6300 = P × 120/100
⇒ P × 120/100 = $6300
⇒ P = 6300/120/100
⇒ P = 6300 × 100/120
⇒ P = 6300 × 100/120
⇒ P = 630000/120
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 6300, then the Principal = 100/120 × 6300
= 100 × 6300/120
= 630000/120
= 5250
Thus, Principal = $5250
Thus, the sum borrowed = $5250 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(2) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?
(3) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?
(5) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
(7) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.
(8) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(9) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?