Question:
How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?
Correct Answer
$6900
Solution And Explanation
Solution
Given,
Amount (A) = $7935
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
$7935 = P (1 + 3% × 5)
⇒ $7935 = P (1 + 3/100 × 5)
⇒ $7935 = P (1 + 3 × 5/100)
⇒ $7935 = P (1 + 15/100)
⇒ $7935 = P (100 + 15/100)
⇒ $7935 = P × 115/100
⇒ P × 115/100 = $7935
⇒ P = 7935/115/100
⇒ P = 7935 × 100/115
⇒ P = 7935 × 100/115
⇒ P = 793500/115
⇒ P = $6900
Thus, the sum borrowed (P) = $6900 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 7935, then the Principal = 100/115 × 7935
= 100 × 7935/115
= 793500/115
= 6900
Thus, Principal = $6900
Thus, the sum borrowed = $6900 Answer
Similar Questions
(1) If Sandra paid $4984 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) What amount will be due after 2 years if John borrowed a sum of $3100 at a 10% simple interest?
(3) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 4 years.
(4) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 8 years.
(6) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?
(7) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?
(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 3 years.
(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 9% simple interest?
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.