Question:
Mark had to pay $4928 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
$4400
Solution And Explanation
Solution
Given,
Amount (A) = $4928
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
$4928 = P (1 + 4% × 3)
⇒ $4928 = P (1 + 4/100 × 3)
⇒ $4928 = P (1 + 4 × 3/100)
⇒ $4928 = P (1 + 12/100)
⇒ $4928 = P (100 + 12/100)
⇒ $4928 = P × 112/100
⇒ P × 112/100 = $4928
⇒ P = 4928/112/100
⇒ P = 4928 × 100/112
⇒ P = 4928 × 100/112
⇒ P = 492800/112
⇒ P = $4400
Thus, the sum borrowed (P) = $4400 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 4928, then the Principal = 100/112 × 4928
= 100 × 4928/112
= 492800/112
= 4400
Thus, Principal = $4400
Thus, the sum borrowed = $4400 Answer
Similar Questions
(1) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.
(4) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?
(5) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(6) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.
(7) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Emily had to pay $5177.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.
(10) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 4% simple interest?