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) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.
(2) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(3) How much loan did Nancy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7380 to clear it?
(4) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.
(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 10% simple interest?
(8) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
(10) If Jessica paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.