Question:
Paul had to pay $4982 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
$4700
Solution And Explanation
Solution
Given,
Amount (A) = $4982
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
$4982 = P (1 + 2% × 3)
⇒ $4982 = P (1 + 2/100 × 3)
⇒ $4982 = P (1 + 2 × 3/100)
⇒ $4982 = P (1 + 6/100)
⇒ $4982 = P (100 + 6/100)
⇒ $4982 = P × 106/100
⇒ P × 106/100 = $4982
⇒ P = 4982/106/100
⇒ P = 4982 × 100/106
⇒ P = 4982 × 100/106
⇒ P = 498200/106
⇒ P = $4700
Thus, the sum borrowed (P) = $4700 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 4982, then the Principal = 100/106 × 4982
= 100 × 4982/106
= 498200/106
= 4700
Thus, Principal = $4700
Thus, the sum borrowed = $4700 Answer
Similar Questions
(1) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 2% simple interest?
(2) Mark had to pay $4928 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 6% simple interest?
(4) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?
(5) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 4% simple interest?
(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.
(7) William had to pay $3815 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) How much loan did Kevin borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8165 to clear it?
(9) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.