Question:
How much loan did Timothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8880 to clear it?
Correct Answer
$7400
Solution And Explanation
Solution
Given,
Amount (A) = $8880
Rate of Simple Interest (R) = 4%
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
$8880 = P (1 + 4% × 5)
⇒ $8880 = P (1 + 4/100 × 5)
⇒ $8880 = P (1 + 4 × 5/100)
⇒ $8880 = P (1 + 20/100)
⇒ $8880 = P (100 + 20/100)
⇒ $8880 = P × 120/100
⇒ P × 120/100 = $8880
⇒ P = 8880/120/100
⇒ P = 8880 × 100/120
⇒ P = 8880 × 100/120
⇒ P = 888000/120
⇒ P = $7400
Thus, the sum borrowed (P) = $7400 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 8880, then the Principal = 100/120 × 8880
= 100 × 8880/120
= 888000/120
= 7400
Thus, Principal = $7400
Thus, the sum borrowed = $7400 Answer
Similar Questions
(1) What amount will be due after 2 years if William borrowed a sum of $3250 at a 4% simple interest?
(2) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(3) Karen had to pay $4305.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.
(5) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 10% simple interest?
(6) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?
(7) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(8) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?
(9) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?
(10) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?