Question : How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?
Correct Answer $7750
Solution & Explanation
Solution
Given,
Amount (A) = $8912.5
Rate of Simple Interest (R) = 3%
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
$8912.5 = P (1 + 3% × 5)
⇒ $8912.5 = P (1 + 3/100 × 5)
⇒ $8912.5 = P (1 + 3 × 5/100)
⇒ $8912.5 = P (1 + 15/100)
⇒ $8912.5 = P (100 + 15/100)
⇒ $8912.5 = P × 115/100
⇒ P × 115/100 = $8912.5
⇒ P = 8912.5/115/100
⇒ P = 8912.5 × 100/115
⇒ P = 8912.5 × 100/115
⇒ P = 891250/115
⇒ P = $7750
Thus, the sum borrowed (P) = $7750 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 8912.5, then the Principal = 100/115 × 8912.5
= 100 × 8912.5/115
= 891250/115
= 7750
Thus, Principal = $7750
Thus, the sum borrowed = $7750 Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?
(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?
(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?
(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 8 years.
(8) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.
(9) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 3 years.