Question:
Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
Correct Answer
$3150
Solution And Explanation
Solution
Given,
Amount (A) = $3528
Rate of Simple Interest (R) = 4%
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
$3528 = P (1 + 4% × 3)
⇒ $3528 = P (1 + 4/100 × 3)
⇒ $3528 = P (1 + 4 × 3/100)
⇒ $3528 = P (1 + 12/100)
⇒ $3528 = P (100 + 12/100)
⇒ $3528 = P × 112/100
⇒ P × 112/100 = $3528
⇒ P = 3528/112/100
⇒ P = 3528 × 100/112
⇒ P = 3528 × 100/112
⇒ P = 352800/112
⇒ P = $3150
Thus, the sum borrowed (P) = $3150 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 12
Thus, simple interest for 3 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 3528, then the Principal = 100/112 × 3528
= 100 × 3528/112
= 352800/112
= 3150
Thus, Principal = $3150
Thus, the sum borrowed = $3150 Answer
Similar Questions
(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.
(2) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6812.5 to clear it?
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.
(4) Linda had to pay $3852.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(6) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(7) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?
(9) How much loan did Betty borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7187.5 to clear it?
(10) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?