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 & 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
(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 4 years.
(3) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.
(4) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 4 years.
(6) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?
(7) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?
(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 6% simple interest?
(9) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.