Question:
How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?
Correct Answer
$6100
Solution And Explanation
Solution
Given,
Amount (A) = $7015
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
$7015 = P (1 + 3% × 5)
⇒ $7015 = P (1 + 3/100 × 5)
⇒ $7015 = P (1 + 3 × 5/100)
⇒ $7015 = P (1 + 15/100)
⇒ $7015 = P (100 + 15/100)
⇒ $7015 = P × 115/100
⇒ P × 115/100 = $7015
⇒ P = 7015/115/100
⇒ P = 7015 × 100/115
⇒ P = 7015 × 100/115
⇒ P = 701500/115
⇒ P = $6100
Thus, the sum borrowed (P) = $6100 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 7015, then the Principal = 100/115 × 7015
= 100 × 7015/115
= 701500/115
= 6100
Thus, Principal = $6100
Thus, the sum borrowed = $6100 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.
(2) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 8 years.
(4) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.
(5) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?
(6) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 3 years.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.
(8) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?
(9) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.
(10) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.