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 Barbara have to pay after 6 years if he takes a loan of $3550 at 4% simple interest?
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 7 years.
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 4 years.
(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.
(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
(6) Susan had to pay $3869 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.
(8) How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?
(9) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?
(10) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?