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) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(2) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 4% simple interest?
(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?
(4) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?
(6) What amount does David have to pay after 5 years if he takes a loan of $3400 at 8% simple interest?
(7) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 7 years.
(9) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 3 years.
(10) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 5% simple interest?