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) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(2) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 7% simple interest?
(4) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
(5) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?
(6) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
(8) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?
(9) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?
(10) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.