Question:
How much loan did Donna borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8220 to clear it?
Correct Answer
$6850
Solution And Explanation
Solution
Given,
Amount (A) = $8220
Rate of Simple Interest (R) = 4%
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
$8220 = P (1 + 4% × 5)
⇒ $8220 = P (1 + 4/100 × 5)
⇒ $8220 = P (1 + 4 × 5/100)
⇒ $8220 = P (1 + 20/100)
⇒ $8220 = P (100 + 20/100)
⇒ $8220 = P × 120/100
⇒ P × 120/100 = $8220
⇒ P = 8220/120/100
⇒ P = 8220 × 100/120
⇒ P = 8220 × 100/120
⇒ P = 822000/120
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 8220, then the Principal = 100/120 × 8220
= 100 × 8220/120
= 822000/120
= 6850
Thus, Principal = $6850
Thus, the sum borrowed = $6850 Answer
Similar Questions
(1) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 4 years.
(2) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.
(4) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?
(6) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9180 to clear it?
(7) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.
(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?
(9) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?
(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?