Question:
How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?
Correct Answer
$5650
Solution And Explanation
Solution
Given,
Amount (A) = $6497.5
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
$6497.5 = P (1 + 3% × 5)
⇒ $6497.5 = P (1 + 3/100 × 5)
⇒ $6497.5 = P (1 + 3 × 5/100)
⇒ $6497.5 = P (1 + 15/100)
⇒ $6497.5 = P (100 + 15/100)
⇒ $6497.5 = P × 115/100
⇒ P × 115/100 = $6497.5
⇒ P = 6497.5/115/100
⇒ P = 6497.5 × 100/115
⇒ P = 6497.5 × 100/115
⇒ P = 649750/115
⇒ P = $5650
Thus, the sum borrowed (P) = $5650 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 6497.5, then the Principal = 100/115 × 6497.5
= 100 × 6497.5/115
= 649750/115
= 5650
Thus, Principal = $5650
Thus, the sum borrowed = $5650 Answer
Similar Questions
(1) If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 8% simple interest?
(3) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(4) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(6) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?
(8) Mark had to pay $4664 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 6% simple interest?
(10) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 3% simple interest?