Question:
How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?
Correct Answer
$7250
Solution And Explanation
Solution
Given,
Amount (A) = $7975
Rate of Simple Interest (R) = 2%
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
$7975 = P (1 + 2% × 5)
⇒ $7975 = P (1 + 2/100 × 5)
⇒ $7975 = P (1 + 2 × 5/100)
⇒ $7975 = P (1 + 10/100)
⇒ $7975 = P (100 + 10/100)
⇒ $7975 = P × 110/100
⇒ P × 110/100 = $7975
⇒ P = 7975/110/100
⇒ P = 7975 × 100/110
⇒ P = 7975 × 100/110
⇒ P = 797500/110
⇒ P = $7250
Thus, the sum borrowed (P) = $7250 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 7975, then the Principal = 100/110 × 7975
= 100 × 7975/110
= 797500/110
= 7250
Thus, Principal = $7250
Thus, the sum borrowed = $7250 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(2) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?
(3) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?
(4) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.
(6) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?
(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?
(8) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?
(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 9% simple interest?
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.