Question:
Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
Correct Answer
$4600
Solution And Explanation
Solution
Given,
Amount (A) = $5152
Rate of Simple Interest (R) = 4%
Time (T) = 3 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
$5152 = P (1 + 4% × 3)
⇒ $5152 = P (1 + 4/100 × 3)
⇒ $5152 = P (1 + 4 × 3/100)
⇒ $5152 = P (1 + 12/100)
⇒ $5152 = P (100 + 12/100)
⇒ $5152 = P × 112/100
⇒ P × 112/100 = $5152
⇒ P = 5152/112/100
⇒ P = 5152 × 100/112
⇒ P = 5152 × 100/112
⇒ P = 515200/112
⇒ P = $4600
Thus, the sum borrowed (P) = $4600 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 = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 4 = 12
Thus, simple interest for 3 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 5152, then the Principal = 100/112 × 5152
= 100 × 5152/112
= 515200/112
= 4600
Thus, Principal = $4600
Thus, the sum borrowed = $4600 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.
(2) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.
(3) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.
(4) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 5% simple interest?
(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?
(6) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 5% simple interest?
(7) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8312.5 to clear it?
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(9) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?
(10) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?