Question:
How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?
Correct Answer
$7750
Solution And Explanation
Solution
Given,
Amount (A) = $8525
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
$8525 = P (1 + 2% × 5)
⇒ $8525 = P (1 + 2/100 × 5)
⇒ $8525 = P (1 + 2 × 5/100)
⇒ $8525 = P (1 + 10/100)
⇒ $8525 = P (100 + 10/100)
⇒ $8525 = P × 110/100
⇒ P × 110/100 = $8525
⇒ P = 8525/110/100
⇒ P = 8525 × 100/110
⇒ P = 8525 × 100/110
⇒ P = 852500/110
⇒ P = $7750
Thus, the sum borrowed (P) = $7750 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 8525, then the Principal = 100/110 × 8525
= 100 × 8525/110
= 852500/110
= 7750
Thus, Principal = $7750
Thus, the sum borrowed = $7750 Answer
Similar Questions
(1) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?
(2) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(4) How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?
(5) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 6% simple interest?
(6) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.
(7) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.
(10) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.