Question:
How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?
Correct Answer
$5150
Solution And Explanation
Solution
Given,
Amount (A) = $5922.5
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
$5922.5 = P (1 + 3% × 5)
⇒ $5922.5 = P (1 + 3/100 × 5)
⇒ $5922.5 = P (1 + 3 × 5/100)
⇒ $5922.5 = P (1 + 15/100)
⇒ $5922.5 = P (100 + 15/100)
⇒ $5922.5 = P × 115/100
⇒ P × 115/100 = $5922.5
⇒ P = 5922.5/115/100
⇒ P = 5922.5 × 100/115
⇒ P = 5922.5 × 100/115
⇒ P = 592250/115
⇒ P = $5150
Thus, the sum borrowed (P) = $5150 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 5922.5, then the Principal = 100/115 × 5922.5
= 100 × 5922.5/115
= 592250/115
= 5150
Thus, Principal = $5150
Thus, the sum borrowed = $5150 Answer
Similar Questions
(1) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?
(2) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 8 years.
(4) What amount does John have to pay after 6 years if he takes a loan of $3200 at 9% simple interest?
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 3 years.
(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 4 years.
(7) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.
(8) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.
(9) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(10) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.