Question:
How much loan did Ashley borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7532.5 to clear it?
Correct Answer
$6550
Solution And Explanation
Solution
Given,
Amount (A) = $7532.5
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
$7532.5 = P (1 + 3% × 5)
⇒ $7532.5 = P (1 + 3/100 × 5)
⇒ $7532.5 = P (1 + 3 × 5/100)
⇒ $7532.5 = P (1 + 15/100)
⇒ $7532.5 = P (100 + 15/100)
⇒ $7532.5 = P × 115/100
⇒ P × 115/100 = $7532.5
⇒ P = 7532.5/115/100
⇒ P = 7532.5 × 100/115
⇒ P = 7532.5 × 100/115
⇒ P = 753250/115
⇒ P = $6550
Thus, the sum borrowed (P) = $6550 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 7532.5, then the Principal = 100/115 × 7532.5
= 100 × 7532.5/115
= 753250/115
= 6550
Thus, Principal = $6550
Thus, the sum borrowed = $6550 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.
(2) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) How much loan did Anthony borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7560 to clear it?
(4) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 2% simple interest?
(5) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.
(6) If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 3 years.
(9) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 4 years.
(10) How much loan did Barbara borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6937.5 to clear it?