Question:
Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
Correct Answer
$4650
Solution And Explanation
Solution
Given,
Amount (A) = $4929
Rate of Simple Interest (R) = 2%
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
$4929 = P (1 + 2% × 3)
⇒ $4929 = P (1 + 2/100 × 3)
⇒ $4929 = P (1 + 2 × 3/100)
⇒ $4929 = P (1 + 6/100)
⇒ $4929 = P (100 + 6/100)
⇒ $4929 = P × 106/100
⇒ P × 106/100 = $4929
⇒ P = 4929/106/100
⇒ P = 4929 × 100/106
⇒ P = 4929 × 100/106
⇒ P = 492900/106
⇒ 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 6
Thus, simple interest for 3 years = 6
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 6 = 106
Calculation of the Principal
Now,
∵ If the Amount is 106, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/106
∴ If the Amount is 4929, then the Principal = 100/106 × 4929
= 100 × 4929/106
= 492900/106
= 4650
Thus, Principal = $4650
Thus, the sum borrowed = $4650 Answer
Similar Questions
(1) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 9% simple interest?
(2) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
(3) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 5% simple interest?
(4) 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?
(5) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) What amount does John have to pay after 5 years if he takes a loan of $3200 at 10% simple interest?
(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 7 years.
(8) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(9) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 10% simple interest?