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 & 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) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 3 years.
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 3 years.
(4) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 3 years.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 8 years.
(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 2% simple interest?
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 8 years.