Question:
Betty had to pay $4632.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
Correct Answer
$4250
Solution And Explanation
Solution
Given,
Amount (A) = $4632.5
Rate of Simple Interest (R) = 3%
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
$4632.5 = P (1 + 3% × 3)
⇒ $4632.5 = P (1 + 3/100 × 3)
⇒ $4632.5 = P (1 + 3 × 3/100)
⇒ $4632.5 = P (1 + 9/100)
⇒ $4632.5 = P (100 + 9/100)
⇒ $4632.5 = P × 109/100
⇒ P × 109/100 = $4632.5
⇒ P = 4632.5/109/100
⇒ P = 4632.5 × 100/109
⇒ P = 4632.5 × 100/109
⇒ P = 463250/109
⇒ P = $4250
Thus, the sum borrowed (P) = $4250 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 4632.5, then the Principal = 100/109 × 4632.5
= 100 × 4632.5/109
= 463250/109
= 4250
Thus, Principal = $4250
Thus, the sum borrowed = $4250 Answer
Similar Questions
(1) Thomas had to pay $4028 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) If Jessica borrowed $3750 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.
(4) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8195 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?
(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?
(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?
(8) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(9) How much loan did James borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6000 to clear it?
(10) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.