Question:
How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?
Correct Answer
$5550
Solution And Explanation
Solution
Given,
Amount (A) = $6105
Rate of Simple Interest (R) = 2%
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
$6105 = P (1 + 2% × 5)
⇒ $6105 = P (1 + 2/100 × 5)
⇒ $6105 = P (1 + 2 × 5/100)
⇒ $6105 = P (1 + 10/100)
⇒ $6105 = P (100 + 10/100)
⇒ $6105 = P × 110/100
⇒ P × 110/100 = $6105
⇒ P = 6105/110/100
⇒ P = 6105 × 100/110
⇒ P = 6105 × 100/110
⇒ P = 610500/110
⇒ P = $5550
Thus, the sum borrowed (P) = $5550 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 6105, then the Principal = 100/110 × 6105
= 100 × 6105/110
= 610500/110
= 5550
Thus, Principal = $5550
Thus, the sum borrowed = $5550 Answer
Similar Questions
(1) Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?
(3) 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.
(4) How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?
(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.
(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.
(7) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 7% simple interest?
(8) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(9) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?
(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 4 years.