Question:
How much loan did Paul borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8375 to clear it?
Correct Answer
$6700
Solution And Explanation
Solution
Given,
Amount (A) = $8375
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
$8375 = P (1 + 5% × 5)
⇒ $8375 = P (1 + 5/100 × 5)
⇒ $8375 = P (1 + 5 × 5/100)
⇒ $8375 = P (1 + 25/100)
⇒ $8375 = P (100 + 25/100)
⇒ $8375 = P × 125/100
⇒ P × 125/100 = $8375
⇒ P = 8375/125/100
⇒ P = 8375 × 100/125
⇒ P = 8375 × 100/125
⇒ P = 837500/125
⇒ P = $6700
Thus, the sum borrowed (P) = $6700 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 8375, then the Principal = 100/125 × 8375
= 100 × 8375/125
= 837500/125
= 6700
Thus, Principal = $6700
Thus, the sum borrowed = $6700 Answer
Similar Questions
(1) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 7% simple interest?
(2) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.
(4) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.
(5) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.
(6) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12670 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 4 years.
(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 3 years.
(9) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?
(10) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.