Question:
Jennifer had to pay $3445 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
Correct Answer
$3250
Solution And Explanation
Solution
Given,
Amount (A) = $3445
Rate of Simple Interest (R) = 2%
Time (T) = 3 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
$3445 = P (1 + 2% × 3)
⇒ $3445 = P (1 + 2/100 × 3)
⇒ $3445 = P (1 + 2 × 3/100)
⇒ $3445 = P (1 + 6/100)
⇒ $3445 = P (100 + 6/100)
⇒ $3445 = P × 106/100
⇒ P × 106/100 = $3445
⇒ P = 3445/106/100
⇒ P = 3445 × 100/106
⇒ P = 3445 × 100/106
⇒ P = 344500/106
⇒ P = $3250
Thus, the sum borrowed (P) = $3250 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 = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 2 = 6
Thus, simple interest for 3 years = 6
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 6 = 106
Calculation of the Principal
Now,
∵ If the Amount is 106, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/106
∴ If the Amount is 3445, then the Principal = 100/106 × 3445
= 100 × 3445/106
= 344500/106
= 3250
Thus, Principal = $3250
Thus, the sum borrowed = $3250 Answer
Similar Questions
(1) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3100 will amount to $3472 at a simple interest of 4% per annum?
(3) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?
(4) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
(5) Michelle had to pay $5395.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?
(8) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.
(10) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.