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) How much loan did Sandra borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8062.5 to clear it?
(2) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?
(3) How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?
(4) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.
(6) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?
(7) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
(9) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?
(10) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.