Question:
How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?
Correct Answer
$7550
Solution And Explanation
Solution
Given,
Amount (A) = $8305
Rate of Simple Interest (R) = 2%
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
$8305 = P (1 + 2% × 5)
⇒ $8305 = P (1 + 2/100 × 5)
⇒ $8305 = P (1 + 2 × 5/100)
⇒ $8305 = P (1 + 10/100)
⇒ $8305 = P (100 + 10/100)
⇒ $8305 = P × 110/100
⇒ P × 110/100 = $8305
⇒ P = 8305/110/100
⇒ P = 8305 × 100/110
⇒ P = 8305 × 100/110
⇒ P = 830500/110
⇒ P = $7550
Thus, the sum borrowed (P) = $7550 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 8305, then the Principal = 100/110 × 8305
= 100 × 8305/110
= 830500/110
= 7550
Thus, Principal = $7550
Thus, the sum borrowed = $7550 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
(2) How much loan did Andrew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8160 to clear it?
(3) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.
(5) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.
(6) If Margaret paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 7 years.
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 4 years.
(10) How much loan did Anthony borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7560 to clear it?