Question:
Michael had to pay $3696 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
$3300
Solution And Explanation
Solution
Given,
Amount (A) = $3696
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
$3696 = P (1 + 4% × 3)
⇒ $3696 = P (1 + 4/100 × 3)
⇒ $3696 = P (1 + 4 × 3/100)
⇒ $3696 = P (1 + 12/100)
⇒ $3696 = P (100 + 12/100)
⇒ $3696 = P × 112/100
⇒ P × 112/100 = $3696
⇒ P = 3696/112/100
⇒ P = 3696 × 100/112
⇒ P = 3696 × 100/112
⇒ P = 369600/112
⇒ P = $3300
Thus, the sum borrowed (P) = $3300 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 3696, then the Principal = 100/112 × 3696
= 100 × 3696/112
= 369600/112
= 3300
Thus, Principal = $3300
Thus, the sum borrowed = $3300 Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 4 years.
(3) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.
(4) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
(5) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 8% simple interest?
(6) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.
(7) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(8) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.
(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?