Question:
How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?
Correct Answer
$5250
Solution And Explanation
Solution
Given,
Amount (A) = $6562.5
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
$6562.5 = P (1 + 5% × 5)
⇒ $6562.5 = P (1 + 5/100 × 5)
⇒ $6562.5 = P (1 + 5 × 5/100)
⇒ $6562.5 = P (1 + 25/100)
⇒ $6562.5 = P (100 + 25/100)
⇒ $6562.5 = P × 125/100
⇒ P × 125/100 = $6562.5
⇒ P = 6562.5/125/100
⇒ P = 6562.5 × 100/125
⇒ P = 6562.5 × 100/125
⇒ P = 656250/125
⇒ P = $5250
Thus, the sum borrowed (P) = $5250 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 6562.5, then the Principal = 100/125 × 6562.5
= 100 × 6562.5/125
= 656250/125
= 5250
Thus, Principal = $5250
Thus, the sum borrowed = $5250 Answer
Similar Questions
(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?
(2) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?
(3) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 3 years.
(5) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?
(6) David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(8) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
(9) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.