Question:
How much loan did Jennifer borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6037.5 to clear it?
Correct Answer
$5250
Solution And Explanation
Solution
Given,
Amount (A) = $6037.5
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
$6037.5 = P (1 + 3% × 5)
⇒ $6037.5 = P (1 + 3/100 × 5)
⇒ $6037.5 = P (1 + 3 × 5/100)
⇒ $6037.5 = P (1 + 15/100)
⇒ $6037.5 = P (100 + 15/100)
⇒ $6037.5 = P × 115/100
⇒ P × 115/100 = $6037.5
⇒ P = 6037.5/115/100
⇒ P = 6037.5 × 100/115
⇒ P = 6037.5 × 100/115
⇒ P = 603750/115
⇒ P = $5250
Thus, the sum borrowed (P) = $5250 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 6037.5, then the Principal = 100/115 × 6037.5
= 100 × 6037.5/115
= 603750/115
= 5250
Thus, Principal = $5250
Thus, the sum borrowed = $5250 Answer
Similar Questions
(1) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) If Margaret paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?
(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 5% simple interest?
(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
(6) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 3% simple interest?
(7) 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.
(8) How much loan did Donna borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8562.5 to clear it?
(9) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?
(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.