Question:
How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?
Correct Answer
$5950
Solution And Explanation
Solution
Given,
Amount (A) = $7437.5
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
$7437.5 = P (1 + 5% × 5)
⇒ $7437.5 = P (1 + 5/100 × 5)
⇒ $7437.5 = P (1 + 5 × 5/100)
⇒ $7437.5 = P (1 + 25/100)
⇒ $7437.5 = P (100 + 25/100)
⇒ $7437.5 = P × 125/100
⇒ P × 125/100 = $7437.5
⇒ P = 7437.5/125/100
⇒ P = 7437.5 × 100/125
⇒ P = 7437.5 × 100/125
⇒ P = 743750/125
⇒ P = $5950
Thus, the sum borrowed (P) = $5950 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 7437.5, then the Principal = 100/125 × 7437.5
= 100 × 7437.5/125
= 743750/125
= 5950
Thus, Principal = $5950
Thus, the sum borrowed = $5950 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.
(2) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?
(3) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.
(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.
(7) Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 8% simple interest?
(9) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?
(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 8 years.