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) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.
(2) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.
(3) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?
(5) If Patricia paid $3402 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?
(7) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?
(8) 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.
(9) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?
(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.