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) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
(2) 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?
(3) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?
(4) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.
(5) How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?
(6) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?
(8) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 6% simple interest?
(9) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?
(10) 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?