Question:
How much loan did Daniel borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6710 to clear it?
Correct Answer
$6100
Solution And Explanation
Solution
Given,
Amount (A) = $6710
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
$6710 = P (1 + 2% × 5)
⇒ $6710 = P (1 + 2/100 × 5)
⇒ $6710 = P (1 + 2 × 5/100)
⇒ $6710 = P (1 + 10/100)
⇒ $6710 = P (100 + 10/100)
⇒ $6710 = P × 110/100
⇒ P × 110/100 = $6710
⇒ P = 6710/110/100
⇒ P = 6710 × 100/110
⇒ P = 6710 × 100/110
⇒ P = 671000/110
⇒ P = $6100
Thus, the sum borrowed (P) = $6100 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 6710, then the Principal = 100/110 × 6710
= 100 × 6710/110
= 671000/110
= 6100
Thus, Principal = $6100
Thus, the sum borrowed = $6100 Answer
Similar Questions
(1) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.
(3) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?
(4) Linda had to pay $3651.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 3 years.
(6) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.
(7) Donald had to pay $4770 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?
(9) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 7 years.
(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 7 years.