Question:
How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?
Correct Answer
$7950
Solution And Explanation
Solution
Given,
Amount (A) = $8745
Rate of Simple Interest (R) = 2%
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
$8745 = P (1 + 2% × 5)
⇒ $8745 = P (1 + 2/100 × 5)
⇒ $8745 = P (1 + 2 × 5/100)
⇒ $8745 = P (1 + 10/100)
⇒ $8745 = P (100 + 10/100)
⇒ $8745 = P × 110/100
⇒ P × 110/100 = $8745
⇒ P = 8745/110/100
⇒ P = 8745 × 100/110
⇒ P = 8745 × 100/110
⇒ P = 874500/110
⇒ P = $7950
Thus, the sum borrowed (P) = $7950 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 8745, then the Principal = 100/110 × 8745
= 100 × 8745/110
= 874500/110
= 7950
Thus, Principal = $7950
Thus, the sum borrowed = $7950 Answer
Similar Questions
(1) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 3 years.
(3) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(4) What amount does John have to pay after 6 years if he takes a loan of $3200 at 6% simple interest?
(5) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.
(6) William had to pay $3815 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 5% simple interest?
(8) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?
(9) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(10) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 7% simple interest?