Question:
Margaret had to pay $4611 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
$4350
Solution And Explanation
Solution
Given,
Amount (A) = $4611
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
$4611 = P (1 + 2% × 3)
⇒ $4611 = P (1 + 2/100 × 3)
⇒ $4611 = P (1 + 2 × 3/100)
⇒ $4611 = P (1 + 6/100)
⇒ $4611 = P (100 + 6/100)
⇒ $4611 = P × 106/100
⇒ P × 106/100 = $4611
⇒ P = 4611/106/100
⇒ P = 4611 × 100/106
⇒ P = 4611 × 100/106
⇒ P = 461100/106
⇒ P = $4350
Thus, the sum borrowed (P) = $4350 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 4611, then the Principal = 100/106 × 4611
= 100 × 4611/106
= 461100/106
= 4350
Thus, Principal = $4350
Thus, the sum borrowed = $4350 Answer
Similar Questions
(1) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?
(2) How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?
(3) How much loan did Nancy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7687.5 to clear it?
(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.
(5) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?
(7) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 3 years.
(9) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 9% simple interest?
(10) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?