Question:
How much loan did Nancy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7687.5 to clear it?
Correct Answer
$6150
Solution And Explanation
Solution
Given,
Amount (A) = $7687.5
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
$7687.5 = P (1 + 5% × 5)
⇒ $7687.5 = P (1 + 5/100 × 5)
⇒ $7687.5 = P (1 + 5 × 5/100)
⇒ $7687.5 = P (1 + 25/100)
⇒ $7687.5 = P (100 + 25/100)
⇒ $7687.5 = P × 125/100
⇒ P × 125/100 = $7687.5
⇒ P = 7687.5/125/100
⇒ P = 7687.5 × 100/125
⇒ P = 7687.5 × 100/125
⇒ P = 768750/125
⇒ P = $6150
Thus, the sum borrowed (P) = $6150 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 7687.5, then the Principal = 100/125 × 7687.5
= 100 × 7687.5/125
= 768750/125
= 6150
Thus, Principal = $6150
Thus, the sum borrowed = $6150 Answer
Similar Questions
(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?
(2) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) What amount does David have to pay after 6 years if he takes a loan of $3400 at 10% simple interest?
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 3 years.
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 8 years.
(6) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9800 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.
(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 3 years.
(10) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 7% simple interest?