Question:
How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?
Correct Answer
$6450
Solution And Explanation
Solution
Given,
Amount (A) = $7417.5
Rate of Simple Interest (R) = 3%
Time (T) = 5 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
$7417.5 = P (1 + 3% × 5)
⇒ $7417.5 = P (1 + 3/100 × 5)
⇒ $7417.5 = P (1 + 3 × 5/100)
⇒ $7417.5 = P (1 + 15/100)
⇒ $7417.5 = P (100 + 15/100)
⇒ $7417.5 = P × 115/100
⇒ P × 115/100 = $7417.5
⇒ P = 7417.5/115/100
⇒ P = 7417.5 × 100/115
⇒ P = 7417.5 × 100/115
⇒ P = 741750/115
⇒ P = $6450
Thus, the sum borrowed (P) = $6450 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 = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 3 = 15
Thus, simple interest for 5 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 7417.5, then the Principal = 100/115 × 7417.5
= 100 × 7417.5/115
= 741750/115
= 6450
Thus, Principal = $6450
Thus, the sum borrowed = $6450 Answer
Similar Questions
(1) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 3 years.
(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?
(3) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.
(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(6) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?
(8) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
(9) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.