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) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.
(2) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.
(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 3% simple interest?
(5) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(6) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 3 years.
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.
(10) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.