Question:
How much loan did Michelle borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7992.5 to clear it?
Correct Answer
$6950
Solution And Explanation
Solution
Given,
Amount (A) = $7992.5
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
$7992.5 = P (1 + 3% × 5)
⇒ $7992.5 = P (1 + 3/100 × 5)
⇒ $7992.5 = P (1 + 3 × 5/100)
⇒ $7992.5 = P (1 + 15/100)
⇒ $7992.5 = P (100 + 15/100)
⇒ $7992.5 = P × 115/100
⇒ P × 115/100 = $7992.5
⇒ P = 7992.5/115/100
⇒ P = 7992.5 × 100/115
⇒ P = 7992.5 × 100/115
⇒ P = 799250/115
⇒ P = $6950
Thus, the sum borrowed (P) = $6950 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 7992.5, then the Principal = 100/115 × 7992.5
= 100 × 7992.5/115
= 799250/115
= 6950
Thus, Principal = $6950
Thus, the sum borrowed = $6950 Answer
Similar Questions
(1) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10430 to clear the loan, then find the time period of the loan.
(2) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?
(3) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.
(5) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(6) If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?
(8) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?
(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 3 years.
(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?