Question:
( 1 of 10 ) How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
$6382.5
Correct Answer
$7400
Solution And Explanation
Solution
Given,
Amount (A) = $8510
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
$8510 = P (1 + 3% × 5)
⇒ $8510 = P (1 + 3/100 × 5)
⇒ $8510 = P (1 + 3 × 5/100)
⇒ $8510 = P (1 + 15/100)
⇒ $8510 = P (100 + 15/100)
⇒ $8510 = P × 115/100
⇒ P × 115/100 = $8510
⇒ P = 8510/115/100
⇒ P = 8510 × 100/115
⇒ P = 8510 × 100/115
⇒ P = 851000/115
⇒ P = $7400
Thus, the sum borrowed (P) = $7400 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 8510, then the Principal = 100/115 × 8510
= 100 × 8510/115
= 851000/115
= 7400
Thus, Principal = $7400
Thus, the sum borrowed = $7400 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.
(2) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 7 years.
(4) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.
(5) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(6) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?
(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 4 years.
(9) Christopher took a loan of $6000 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.
(10) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.