Question:
Kimberly had to pay $5208 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
$4650
Solution And Explanation
Solution
Given,
Amount (A) = $5208
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
$5208 = P (1 + 4% × 3)
⇒ $5208 = P (1 + 4/100 × 3)
⇒ $5208 = P (1 + 4 × 3/100)
⇒ $5208 = P (1 + 12/100)
⇒ $5208 = P (100 + 12/100)
⇒ $5208 = P × 112/100
⇒ P × 112/100 = $5208
⇒ P = 5208/112/100
⇒ P = 5208 × 100/112
⇒ P = 5208 × 100/112
⇒ P = 520800/112
⇒ P = $4650
Thus, the sum borrowed (P) = $4650 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 5208, then the Principal = 100/112 × 5208
= 100 × 5208/112
= 520800/112
= 4650
Thus, Principal = $4650
Thus, the sum borrowed = $4650 Answer
Similar Questions
(1) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.
(2) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?
(3) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?
(4) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?
(5) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 8 years.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.
(7) If Patricia paid $3780 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 Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?
(9) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 2% simple interest?
(10) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 6% simple interest?