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) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 5% simple interest?
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.
(3) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?
(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?
(5) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(6) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?
(7) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
(9) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 8 years.