Question:
How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?
Correct Answer
$7850
Solution And Explanation
Solution
Given,
Amount (A) = $9027.5
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
$9027.5 = P (1 + 3% × 5)
⇒ $9027.5 = P (1 + 3/100 × 5)
⇒ $9027.5 = P (1 + 3 × 5/100)
⇒ $9027.5 = P (1 + 15/100)
⇒ $9027.5 = P (100 + 15/100)
⇒ $9027.5 = P × 115/100
⇒ P × 115/100 = $9027.5
⇒ P = 9027.5/115/100
⇒ P = 9027.5 × 100/115
⇒ P = 9027.5 × 100/115
⇒ P = 902750/115
⇒ P = $7850
Thus, the sum borrowed (P) = $7850 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 9027.5, then the Principal = 100/115 × 9027.5
= 100 × 9027.5/115
= 902750/115
= 7850
Thus, Principal = $7850
Thus, the sum borrowed = $7850 Answer
Similar Questions
(1) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 3 years.
(4) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(5) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 2% simple interest?
(6) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 4 years.
(7) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.
(8) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?
(9) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 8 years.
(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 4 years.