Question:
How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?
Correct Answer
$5700
Solution And Explanation
Solution
Given,
Amount (A) = $6555
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
$6555 = P (1 + 3% × 5)
⇒ $6555 = P (1 + 3/100 × 5)
⇒ $6555 = P (1 + 3 × 5/100)
⇒ $6555 = P (1 + 15/100)
⇒ $6555 = P (100 + 15/100)
⇒ $6555 = P × 115/100
⇒ P × 115/100 = $6555
⇒ P = 6555/115/100
⇒ P = 6555 × 100/115
⇒ P = 6555 × 100/115
⇒ P = 655500/115
⇒ P = $5700
Thus, the sum borrowed (P) = $5700 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 6555, then the Principal = 100/115 × 6555
= 100 × 6555/115
= 655500/115
= 5700
Thus, Principal = $5700
Thus, the sum borrowed = $5700 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.
(2) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?
(3) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.
(5) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?
(7) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 7 years.
(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(10) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.