Question:
How much loan did Donna borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7535 to clear it?
Correct Answer
$6850
Solution And Explanation
Solution
Given,
Amount (A) = $7535
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
$7535 = P (1 + 2% × 5)
⇒ $7535 = P (1 + 2/100 × 5)
⇒ $7535 = P (1 + 2 × 5/100)
⇒ $7535 = P (1 + 10/100)
⇒ $7535 = P (100 + 10/100)
⇒ $7535 = P × 110/100
⇒ P × 110/100 = $7535
⇒ P = 7535/110/100
⇒ P = 7535 × 100/110
⇒ P = 7535 × 100/110
⇒ P = 753500/110
⇒ P = $6850
Thus, the sum borrowed (P) = $6850 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 7535, then the Principal = 100/110 × 7535
= 100 × 7535/110
= 753500/110
= 6850
Thus, Principal = $6850
Thus, the sum borrowed = $6850 Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 4 years.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.
(4) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 8% simple interest?
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 7 years.
(6) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?
(8) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.
(9) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.