Question:
How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?
Correct Answer
$5050
Solution And Explanation
Solution
Given,
Amount (A) = $6060
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
$6060 = P (1 + 4% × 5)
⇒ $6060 = P (1 + 4/100 × 5)
⇒ $6060 = P (1 + 4 × 5/100)
⇒ $6060 = P (1 + 20/100)
⇒ $6060 = P (100 + 20/100)
⇒ $6060 = P × 120/100
⇒ P × 120/100 = $6060
⇒ P = 6060/120/100
⇒ P = 6060 × 100/120
⇒ P = 6060 × 100/120
⇒ P = 606000/120
⇒ P = $5050
Thus, the sum borrowed (P) = $5050 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 6060, then the Principal = 100/120 × 6060
= 100 × 6060/120
= 606000/120
= 5050
Thus, Principal = $5050
Thus, the sum borrowed = $5050 Answer
Similar Questions
(1) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 5% simple interest.
(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 6% simple interest?
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.
(4) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 8% simple interest?
(5) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 10% simple interest?
(6) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 9% simple interest?
(8) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
(10) If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.