Question:
How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?
Correct Answer
$7250
Solution And Explanation
Solution
Given,
Amount (A) = $8700
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
$8700 = P (1 + 4% × 5)
⇒ $8700 = P (1 + 4/100 × 5)
⇒ $8700 = P (1 + 4 × 5/100)
⇒ $8700 = P (1 + 20/100)
⇒ $8700 = P (100 + 20/100)
⇒ $8700 = P × 120/100
⇒ P × 120/100 = $8700
⇒ P = 8700/120/100
⇒ P = 8700 × 100/120
⇒ P = 8700 × 100/120
⇒ P = 870000/120
⇒ P = $7250
Thus, the sum borrowed (P) = $7250 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 8700, then the Principal = 100/120 × 8700
= 100 × 8700/120
= 870000/120
= 7250
Thus, Principal = $7250
Thus, the sum borrowed = $7250 Answer
Similar Questions
(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 4 years.
(3) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?
(4) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.
(6) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
(7) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 4% simple interest?
(9) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?
(10) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.