Question:
How much loan did Andrew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8160 to clear it?
Correct Answer
$6800
Solution And Explanation
Solution
Given,
Amount (A) = $8160
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
$8160 = P (1 + 4% × 5)
⇒ $8160 = P (1 + 4/100 × 5)
⇒ $8160 = P (1 + 4 × 5/100)
⇒ $8160 = P (1 + 20/100)
⇒ $8160 = P (100 + 20/100)
⇒ $8160 = P × 120/100
⇒ P × 120/100 = $8160
⇒ P = 8160/120/100
⇒ P = 8160 × 100/120
⇒ P = 8160 × 100/120
⇒ P = 816000/120
⇒ P = $6800
Thus, the sum borrowed (P) = $6800 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 8160, then the Principal = 100/120 × 8160
= 100 × 8160/120
= 816000/120
= 6800
Thus, Principal = $6800
Thus, the sum borrowed = $6800 Answer
Similar Questions
(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.
(2) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.
(3) Nancy had to pay $4772.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 8% simple interest?
(5) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 8% simple interest?
(6) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.
(8) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8528 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
(10) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 6% simple interest?