Question:
How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?
Correct Answer
$6650
Solution And Explanation
Solution
Given,
Amount (A) = $7647.5
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
$7647.5 = P (1 + 3% × 5)
⇒ $7647.5 = P (1 + 3/100 × 5)
⇒ $7647.5 = P (1 + 3 × 5/100)
⇒ $7647.5 = P (1 + 15/100)
⇒ $7647.5 = P (100 + 15/100)
⇒ $7647.5 = P × 115/100
⇒ P × 115/100 = $7647.5
⇒ P = 7647.5/115/100
⇒ P = 7647.5 × 100/115
⇒ P = 7647.5 × 100/115
⇒ P = 764750/115
⇒ P = $6650
Thus, the sum borrowed (P) = $6650 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 7647.5, then the Principal = 100/115 × 7647.5
= 100 × 7647.5/115
= 764750/115
= 6650
Thus, Principal = $6650
Thus, the sum borrowed = $6650 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.
(2) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 3% simple interest?
(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?
(5) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.
(6) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.
(7) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(8) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?
(9) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.