Question:
Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
Correct Answer
$3850
Solution And Explanation
Solution
Given,
Amount (A) = $4427.5
Rate of Simple Interest (R) = 5%
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
$4427.5 = P (1 + 5% × 3)
⇒ $4427.5 = P (1 + 5/100 × 3)
⇒ $4427.5 = P (1 + 5 × 3/100)
⇒ $4427.5 = P (1 + 15/100)
⇒ $4427.5 = P (100 + 15/100)
⇒ $4427.5 = P × 115/100
⇒ P × 115/100 = $4427.5
⇒ P = 4427.5/115/100
⇒ P = 4427.5 × 100/115
⇒ P = 4427.5 × 100/115
⇒ P = 442750/115
⇒ P = $3850
Thus, the sum borrowed (P) = $3850 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 15
Thus, simple interest for 3 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 4427.5, then the Principal = 100/115 × 4427.5
= 100 × 4427.5/115
= 442750/115
= 3850
Thus, Principal = $3850
Thus, the sum borrowed = $3850 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.
(2) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(3) How much loan did Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?
(4) James had to pay $3270 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 4 years.
(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
(7) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(9) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 6% simple interest?
(10) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.