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) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 10% simple interest?
(2) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?
(3) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.
(4) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?
(5) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.
(6) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(7) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(8) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 8 years.
(10) Jennifer had to pay $3640 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.