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 Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?
(2) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 7% simple interest?
(3) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(4) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?
(6) Mark had to pay $4928 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 if Linda borrowed a sum of $3350 at 5% simple interest for 3 years.
(8) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(10) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?