Question:
Mary had to pay $3507.5 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
$3050
Solution And Explanation
Solution
Given,
Amount (A) = $3507.5
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
$3507.5 = P (1 + 5% × 3)
⇒ $3507.5 = P (1 + 5/100 × 3)
⇒ $3507.5 = P (1 + 5 × 3/100)
⇒ $3507.5 = P (1 + 15/100)
⇒ $3507.5 = P (100 + 15/100)
⇒ $3507.5 = P × 115/100
⇒ P × 115/100 = $3507.5
⇒ P = 3507.5/115/100
⇒ P = 3507.5 × 100/115
⇒ P = 3507.5 × 100/115
⇒ P = 350750/115
⇒ P = $3050
Thus, the sum borrowed (P) = $3050 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 3507.5, then the Principal = 100/115 × 3507.5
= 100 × 3507.5/115
= 350750/115
= 3050
Thus, Principal = $3050
Thus, the sum borrowed = $3050 Answer
Similar Questions
(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?
(2) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 3 years.
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.
(4) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.
(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(6) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?
(8) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 6% simple interest?
(9) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?
(10) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 4 years.