Question:
How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?
Correct Answer
$5700
Solution And Explanation
Solution
Given,
Amount (A) = $6555
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
$6555 = P (1 + 3% × 5)
⇒ $6555 = P (1 + 3/100 × 5)
⇒ $6555 = P (1 + 3 × 5/100)
⇒ $6555 = P (1 + 15/100)
⇒ $6555 = P (100 + 15/100)
⇒ $6555 = P × 115/100
⇒ P × 115/100 = $6555
⇒ P = 6555/115/100
⇒ P = 6555 × 100/115
⇒ P = 6555 × 100/115
⇒ P = 655500/115
⇒ 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 = 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 6555, then the Principal = 100/115 × 6555
= 100 × 6555/115
= 655500/115
= 5700
Thus, Principal = $5700
Thus, the sum borrowed = $5700 Answer
Similar Questions
(1) If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(2) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(3) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 10% simple interest?
(4) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 8% simple interest?
(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 6% simple interest?
(6) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 8 years.
(8) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 4 years.
(9) James had to pay $3360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?