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) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 7 years.
(3) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 8 years.
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.
(6) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.
(9) What amount does James have to pay after 6 years if he takes a loan of $3000 at 4% simple interest?
(10) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.