Question:
How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?
Correct Answer
$5700
Solution And Explanation
Solution
Given,
Amount (A) = $6840
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
$6840 = P (1 + 4% × 5)
⇒ $6840 = P (1 + 4/100 × 5)
⇒ $6840 = P (1 + 4 × 5/100)
⇒ $6840 = P (1 + 20/100)
⇒ $6840 = P (100 + 20/100)
⇒ $6840 = P × 120/100
⇒ P × 120/100 = $6840
⇒ P = 6840/120/100
⇒ P = 6840 × 100/120
⇒ P = 6840 × 100/120
⇒ P = 684000/120
⇒ P = $5700
Thus, the sum borrowed (P) = $5700 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 6840, then the Principal = 100/120 × 6840
= 100 × 6840/120
= 684000/120
= 5700
Thus, Principal = $5700
Thus, the sum borrowed = $5700 Answer
Similar Questions
(1) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?
(2) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 3% simple interest?
(3) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(4) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?
(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 4 years.
(7) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?
(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(9) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.
(10) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 3% simple interest?