Question:
How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?
Correct Answer
$7450
Solution And Explanation
Solution
Given,
Amount (A) = $8567.5
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
$8567.5 = P (1 + 3% × 5)
⇒ $8567.5 = P (1 + 3/100 × 5)
⇒ $8567.5 = P (1 + 3 × 5/100)
⇒ $8567.5 = P (1 + 15/100)
⇒ $8567.5 = P (100 + 15/100)
⇒ $8567.5 = P × 115/100
⇒ P × 115/100 = $8567.5
⇒ P = 8567.5/115/100
⇒ P = 8567.5 × 100/115
⇒ P = 8567.5 × 100/115
⇒ P = 856750/115
⇒ P = $7450
Thus, the sum borrowed (P) = $7450 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 8567.5, then the Principal = 100/115 × 8567.5
= 100 × 8567.5/115
= 856750/115
= 7450
Thus, Principal = $7450
Thus, the sum borrowed = $7450 Answer
Similar Questions
(1) Jessica had to pay $4087.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?
(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 4 years.
(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.
(6) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 9% simple interest?
(7) How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?
(8) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(9) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?