Question:
How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?
Correct Answer
$7450
Solution And Explanation
Solution
Given,
Amount (A) = $8567.5
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
$8567.5 = P (1 + 3% × 5)
⇒ $8567.5 = P (1 + 3/100 × 5)
⇒ $8567.5 = P (1 + 3 × 5/100)
⇒ $8567.5 = P (1 + 15/100)
⇒ $8567.5 = P (100 + 15/100)
⇒ $8567.5 = P × 115/100
⇒ P × 115/100 = $8567.5
⇒ P = 8567.5/115/100
⇒ P = 8567.5 × 100/115
⇒ P = 8567.5 × 100/115
⇒ P = 856750/115
⇒ P = $7450
Thus, the sum borrowed (P) = $7450 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 8567.5, then the Principal = 100/115 × 8567.5
= 100 × 8567.5/115
= 856750/115
= 7450
Thus, Principal = $7450
Thus, the sum borrowed = $7450 Answer
Similar Questions
(1) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?
(2) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
(3) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?
(4) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.
(5) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(6) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?
(7) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.
(10) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?