Question:
How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?
Correct Answer
$7350
Solution And Explanation
Solution
Given,
Amount (A) = $8452.5
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
$8452.5 = P (1 + 3% × 5)
⇒ $8452.5 = P (1 + 3/100 × 5)
⇒ $8452.5 = P (1 + 3 × 5/100)
⇒ $8452.5 = P (1 + 15/100)
⇒ $8452.5 = P (100 + 15/100)
⇒ $8452.5 = P × 115/100
⇒ P × 115/100 = $8452.5
⇒ P = 8452.5/115/100
⇒ P = 8452.5 × 100/115
⇒ P = 8452.5 × 100/115
⇒ P = 845250/115
⇒ P = $7350
Thus, the sum borrowed (P) = $7350 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 8452.5, then the Principal = 100/115 × 8452.5
= 100 × 8452.5/115
= 845250/115
= 7350
Thus, Principal = $7350
Thus, the sum borrowed = $7350 Answer
Similar Questions
(1) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?
(2) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10860 to clear the loan, then find the time period of the loan.
(3) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?
(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?
(5) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 4 years.
(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(8) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?
(9) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 2% simple interest?
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.