Question:
How much loan did Kimberly borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8312.5 to clear it?
Correct Answer
$6650
Solution And Explanation
Solution
Given,
Amount (A) = $8312.5
Rate of Simple Interest (R) = 5%
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
$8312.5 = P (1 + 5% × 5)
⇒ $8312.5 = P (1 + 5/100 × 5)
⇒ $8312.5 = P (1 + 5 × 5/100)
⇒ $8312.5 = P (1 + 25/100)
⇒ $8312.5 = P (100 + 25/100)
⇒ $8312.5 = P × 125/100
⇒ P × 125/100 = $8312.5
⇒ P = 8312.5/125/100
⇒ P = 8312.5 × 100/125
⇒ P = 8312.5 × 100/125
⇒ P = 831250/125
⇒ P = $6650
Thus, the sum borrowed (P) = $6650 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 8312.5, then the Principal = 100/125 × 8312.5
= 100 × 8312.5/125
= 831250/125
= 6650
Thus, Principal = $6650
Thus, the sum borrowed = $6650 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.
(3) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(4) Jennifer had to pay $3445 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 4% simple interest?
(6) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(7) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 8 years.
(9) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(10) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8312.5 to clear it?