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 And 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) How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?
(2) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.
(3) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 8% simple interest?
(4) What amount will be due after 2 years if William borrowed a sum of $3250 at a 6% simple interest?
(5) What amount does John have to pay after 5 years if he takes a loan of $3200 at 9% simple interest?
(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.
(7) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.
(8) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 10% simple interest?
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 8 years.
(10) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.