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) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(2) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
(4) In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?
(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 7 years.
(7) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 3 years.
(8) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.
(9) If David borrowed $3400 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.