Question:
How much loan did Jessica borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6612.5 to clear it?
Correct Answer
$5750
Solution And Explanation
Solution
Given,
Amount (A) = $6612.5
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
$6612.5 = P (1 + 3% × 5)
⇒ $6612.5 = P (1 + 3/100 × 5)
⇒ $6612.5 = P (1 + 3 × 5/100)
⇒ $6612.5 = P (1 + 15/100)
⇒ $6612.5 = P (100 + 15/100)
⇒ $6612.5 = P × 115/100
⇒ P × 115/100 = $6612.5
⇒ P = 6612.5/115/100
⇒ P = 6612.5 × 100/115
⇒ P = 6612.5 × 100/115
⇒ P = 661250/115
⇒ P = $5750
Thus, the sum borrowed (P) = $5750 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 6612.5, then the Principal = 100/115 × 6612.5
= 100 × 6612.5/115
= 661250/115
= 5750
Thus, Principal = $5750
Thus, the sum borrowed = $5750 Answer
Similar Questions
(1) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(3) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.
(4) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 8% simple interest?
(5) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(7) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 9% simple interest?
(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 8% simple interest?
(9) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 6% simple interest?