Question:
Robert had to pay $3286 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
$3100
Solution And Explanation
Solution
Given,
Amount (A) = $3286
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
$3286 = P (1 + 2% × 3)
⇒ $3286 = P (1 + 2/100 × 3)
⇒ $3286 = P (1 + 2 × 3/100)
⇒ $3286 = P (1 + 6/100)
⇒ $3286 = P (100 + 6/100)
⇒ $3286 = P × 106/100
⇒ P × 106/100 = $3286
⇒ P = 3286/106/100
⇒ P = 3286 × 100/106
⇒ P = 3286 × 100/106
⇒ P = 328600/106
⇒ P = $3100
Thus, the sum borrowed (P) = $3100 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 3286, then the Principal = 100/106 × 3286
= 100 × 3286/106
= 328600/106
= 3100
Thus, Principal = $3100
Thus, the sum borrowed = $3100 Answer
Similar Questions
(1) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 8 years.
(2) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(3) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 4 years.
(5) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 8 years.
(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?
(8) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7616 to clear the loan, then find the time period of the loan.
(9) How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?
(10) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.