Question:
Susan had to pay $3978.5 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
$3650
Solution And Explanation
Solution
Given,
Amount (A) = $3978.5
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
$3978.5 = P (1 + 3% × 3)
⇒ $3978.5 = P (1 + 3/100 × 3)
⇒ $3978.5 = P (1 + 3 × 3/100)
⇒ $3978.5 = P (1 + 9/100)
⇒ $3978.5 = P (100 + 9/100)
⇒ $3978.5 = P × 109/100
⇒ P × 109/100 = $3978.5
⇒ P = 3978.5/109/100
⇒ P = 3978.5 × 100/109
⇒ P = 3978.5 × 100/109
⇒ P = 397850/109
⇒ P = $3650
Thus, the sum borrowed (P) = $3650 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 3978.5, then the Principal = 100/109 × 3978.5
= 100 × 3978.5/109
= 397850/109
= 3650
Thus, Principal = $3650
Thus, the sum borrowed = $3650 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
(2) 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.
(3) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 7 years.
(5) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 3 years.
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 8 years.
(8) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?
(9) How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?
(10) If Barbara borrowed $3550 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.