Question:
How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?
Correct Answer
$7900
Solution And Explanation
Solution
Given,
Amount (A) = $9085
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
$9085 = P (1 + 3% × 5)
⇒ $9085 = P (1 + 3/100 × 5)
⇒ $9085 = P (1 + 3 × 5/100)
⇒ $9085 = P (1 + 15/100)
⇒ $9085 = P (100 + 15/100)
⇒ $9085 = P × 115/100
⇒ P × 115/100 = $9085
⇒ P = 9085/115/100
⇒ P = 9085 × 100/115
⇒ P = 9085 × 100/115
⇒ P = 908500/115
⇒ P = $7900
Thus, the sum borrowed (P) = $7900 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 9085, then the Principal = 100/115 × 9085
= 100 × 9085/115
= 908500/115
= 7900
Thus, Principal = $7900
Thus, the sum borrowed = $7900 Answer
Similar Questions
(1) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 3 years.
(2) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?
(3) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.
(4) How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.
(6) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 3 years.
(7) If Kenneth paid $5800 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(10) What amount does David have to pay after 6 years if he takes a loan of $3400 at 4% simple interest?