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) How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.
(3) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?
(4) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.
(6) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?
(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.
(8) What amount will be due after 2 years if David borrowed a sum of $3200 at a 6% simple interest?
(9) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 3% simple interest?
(10) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?