Question:
Susan had to pay $4088 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
$3650
Solution And Explanation
Solution
Given,
Amount (A) = $4088
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
$4088 = P (1 + 4% × 3)
⇒ $4088 = P (1 + 4/100 × 3)
⇒ $4088 = P (1 + 4 × 3/100)
⇒ $4088 = P (1 + 12/100)
⇒ $4088 = P (100 + 12/100)
⇒ $4088 = P × 112/100
⇒ P × 112/100 = $4088
⇒ P = 4088/112/100
⇒ P = 4088 × 100/112
⇒ P = 4088 × 100/112
⇒ P = 408800/112
⇒ P = $3650
Thus, the sum borrowed (P) = $3650 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 4088, then the Principal = 100/112 × 4088
= 100 × 4088/112
= 408800/112
= 3650
Thus, Principal = $3650
Thus, the sum borrowed = $3650 Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 4 years.
(2) If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 3% simple interest?
(4) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?
(5) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.
(8) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 3 years.