Question:
Sarah had to pay $4312 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
$3850
Solution And Explanation
Solution
Given,
Amount (A) = $4312
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
$4312 = P (1 + 4% × 3)
⇒ $4312 = P (1 + 4/100 × 3)
⇒ $4312 = P (1 + 4 × 3/100)
⇒ $4312 = P (1 + 12/100)
⇒ $4312 = P (100 + 12/100)
⇒ $4312 = P × 112/100
⇒ P × 112/100 = $4312
⇒ P = 4312/112/100
⇒ P = 4312 × 100/112
⇒ P = 4312 × 100/112
⇒ P = 431200/112
⇒ P = $3850
Thus, the sum borrowed (P) = $3850 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 4312, then the Principal = 100/112 × 4312
= 100 × 4312/112
= 431200/112
= 3850
Thus, Principal = $3850
Thus, the sum borrowed = $3850 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(2) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?
(3) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?
(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 6% simple interest?
(5) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 8% simple interest?
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 4 years.
(7) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.
(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?