Question:
How much loan did Kimberly borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7980 to clear it?
Correct Answer
$6650
Solution And Explanation
Solution
Given,
Amount (A) = $7980
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
$7980 = P (1 + 4% × 5)
⇒ $7980 = P (1 + 4/100 × 5)
⇒ $7980 = P (1 + 4 × 5/100)
⇒ $7980 = P (1 + 20/100)
⇒ $7980 = P (100 + 20/100)
⇒ $7980 = P × 120/100
⇒ P × 120/100 = $7980
⇒ P = 7980/120/100
⇒ P = 7980 × 100/120
⇒ P = 7980 × 100/120
⇒ P = 798000/120
⇒ 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 = 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 7980, then the Principal = 100/120 × 7980
= 100 × 7980/120
= 798000/120
= 6650
Thus, Principal = $6650
Thus, the sum borrowed = $6650 Answer
Similar Questions
(1) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 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) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 3 years.
(4) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.
(5) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.
(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.
(8) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 10% simple interest?
(9) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 5% simple interest?
(10) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.