Question:
How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?
Correct Answer
$6950
Solution And Explanation
Solution
Given,
Amount (A) = $8687.5
Rate of Simple Interest (R) = 5%
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
$8687.5 = P (1 + 5% × 5)
⇒ $8687.5 = P (1 + 5/100 × 5)
⇒ $8687.5 = P (1 + 5 × 5/100)
⇒ $8687.5 = P (1 + 25/100)
⇒ $8687.5 = P (100 + 25/100)
⇒ $8687.5 = P × 125/100
⇒ P × 125/100 = $8687.5
⇒ P = 8687.5/125/100
⇒ P = 8687.5 × 100/125
⇒ P = 8687.5 × 100/125
⇒ P = 868750/125
⇒ P = $6950
Thus, the sum borrowed (P) = $6950 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 8687.5, then the Principal = 100/125 × 8687.5
= 100 × 8687.5/125
= 868750/125
= 6950
Thus, Principal = $6950
Thus, the sum borrowed = $6950 Answer
Similar Questions
(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 3 years.
(2) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 2% simple interest?
(3) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?
(4) How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 3 years.
(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?
(7) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(8) How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 7 years.
(10) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.