Question:
How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?
Correct Answer
$5100
Solution And Explanation
Solution
Given,
Amount (A) = $5610
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
$5610 = P (1 + 2% × 5)
⇒ $5610 = P (1 + 2/100 × 5)
⇒ $5610 = P (1 + 2 × 5/100)
⇒ $5610 = P (1 + 10/100)
⇒ $5610 = P (100 + 10/100)
⇒ $5610 = P × 110/100
⇒ P × 110/100 = $5610
⇒ P = 5610/110/100
⇒ P = 5610 × 100/110
⇒ P = 5610 × 100/110
⇒ P = 561000/110
⇒ P = $5100
Thus, the sum borrowed (P) = $5100 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 5610, then the Principal = 100/110 × 5610
= 100 × 5610/110
= 561000/110
= 5100
Thus, Principal = $5100
Thus, the sum borrowed = $5100 Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.
(2) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 7 years.
(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?
(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 4% simple interest?
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 7 years.
(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.
(9) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(10) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?