Question:
How much loan did Sharon borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9687.5 to clear it?
Correct Answer
$7750
Solution And Explanation
Solution
Given,
Amount (A) = $9687.5
Rate of Simple Interest (R) = 5%
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
$9687.5 = P (1 + 5% × 5)
⇒ $9687.5 = P (1 + 5/100 × 5)
⇒ $9687.5 = P (1 + 5 × 5/100)
⇒ $9687.5 = P (1 + 25/100)
⇒ $9687.5 = P (100 + 25/100)
⇒ $9687.5 = P × 125/100
⇒ P × 125/100 = $9687.5
⇒ P = 9687.5/125/100
⇒ P = 9687.5 × 100/125
⇒ P = 9687.5 × 100/125
⇒ P = 968750/125
⇒ P = $7750
Thus, the sum borrowed (P) = $7750 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 9687.5, then the Principal = 100/125 × 9687.5
= 100 × 9687.5/125
= 968750/125
= 7750
Thus, Principal = $7750
Thus, the sum borrowed = $7750 Answer
Similar Questions
(1) Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.
(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?
(4) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.
(6) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 8% simple interest?
(8) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.
(10) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?