Question:
How much loan did Amanda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8222.5 to clear it?
Correct Answer
$7150
Solution And Explanation
Solution
Given,
Amount (A) = $8222.5
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
$8222.5 = P (1 + 3% × 5)
⇒ $8222.5 = P (1 + 3/100 × 5)
⇒ $8222.5 = P (1 + 3 × 5/100)
⇒ $8222.5 = P (1 + 15/100)
⇒ $8222.5 = P (100 + 15/100)
⇒ $8222.5 = P × 115/100
⇒ P × 115/100 = $8222.5
⇒ P = 8222.5/115/100
⇒ P = 8222.5 × 100/115
⇒ P = 8222.5 × 100/115
⇒ P = 822250/115
⇒ P = $7150
Thus, the sum borrowed (P) = $7150 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 8222.5, then the Principal = 100/115 × 8222.5
= 100 × 8222.5/115
= 822250/115
= 7150
Thus, Principal = $7150
Thus, the sum borrowed = $7150 Answer
Similar Questions
(1) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(3) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 9% simple interest?
(5) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 10% simple interest?
(6) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.
(7) If James borrowed $3000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(8) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 6% simple interest?
(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.