Question:
How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?
Correct Answer
$7500
Solution And Explanation
Solution
Given,
Amount (A) = $8625
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
$8625 = P (1 + 3% × 5)
⇒ $8625 = P (1 + 3/100 × 5)
⇒ $8625 = P (1 + 3 × 5/100)
⇒ $8625 = P (1 + 15/100)
⇒ $8625 = P (100 + 15/100)
⇒ $8625 = P × 115/100
⇒ P × 115/100 = $8625
⇒ P = 8625/115/100
⇒ P = 8625 × 100/115
⇒ P = 8625 × 100/115
⇒ P = 862500/115
⇒ P = $7500
Thus, the sum borrowed (P) = $7500 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 8625, then the Principal = 100/115 × 8625
= 100 × 8625/115
= 862500/115
= 7500
Thus, Principal = $7500
Thus, the sum borrowed = $7500 Answer
Similar Questions
(1) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 3 years.
(2) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 8% simple interest?
(4) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.
(5) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?
(6) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 3% simple interest?
(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 5% simple interest?
(8) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 years.
(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 7 years.