Question:
How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?
Correct Answer
$7800
Solution And Explanation
Solution
Given,
Amount (A) = $8580
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
$8580 = P (1 + 2% × 5)
⇒ $8580 = P (1 + 2/100 × 5)
⇒ $8580 = P (1 + 2 × 5/100)
⇒ $8580 = P (1 + 10/100)
⇒ $8580 = P (100 + 10/100)
⇒ $8580 = P × 110/100
⇒ P × 110/100 = $8580
⇒ P = 8580/110/100
⇒ P = 8580 × 100/110
⇒ P = 8580 × 100/110
⇒ P = 858000/110
⇒ P = $7800
Thus, the sum borrowed (P) = $7800 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 8580, then the Principal = 100/110 × 8580
= 100 × 8580/110
= 858000/110
= 7800
Thus, Principal = $7800
Thus, the sum borrowed = $7800 Answer
Similar Questions
(1) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(3) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(5) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(6) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?
(7) What amount does William have to pay after 5 years if he takes a loan of $3500 at 9% simple interest?
(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?
(9) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?
(10) What amount does William have to pay after 5 years if he takes a loan of $3500 at 5% simple interest?