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) What amount does John have to pay after 5 years if he takes a loan of $3200 at 7% simple interest?
(2) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 8 years.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.
(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?
(7) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 7 years.
(10) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.