Question:
How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?
Correct Answer
$7900
Solution And Explanation
Solution
Given,
Amount (A) = $9480
Rate of Simple Interest (R) = 4%
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
$9480 = P (1 + 4% × 5)
⇒ $9480 = P (1 + 4/100 × 5)
⇒ $9480 = P (1 + 4 × 5/100)
⇒ $9480 = P (1 + 20/100)
⇒ $9480 = P (100 + 20/100)
⇒ $9480 = P × 120/100
⇒ P × 120/100 = $9480
⇒ P = 9480/120/100
⇒ P = 9480 × 100/120
⇒ P = 9480 × 100/120
⇒ P = 948000/120
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 9480, then the Principal = 100/120 × 9480
= 100 × 9480/120
= 948000/120
= 7900
Thus, Principal = $7900
Thus, the sum borrowed = $7900 Answer
Similar Questions
(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 3% simple interest?
(2) Margaret had to pay $4741.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 3 years.
(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.
(5) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 7 years.
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.
(8) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.
(9) How much loan did Richard borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7000 to clear it?
(10) If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.