Question:
Mary had to pay $3416 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
$3050
Solution And Explanation
Solution
Given,
Amount (A) = $3416
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
$3416 = P (1 + 4% × 3)
⇒ $3416 = P (1 + 4/100 × 3)
⇒ $3416 = P (1 + 4 × 3/100)
⇒ $3416 = P (1 + 12/100)
⇒ $3416 = P (100 + 12/100)
⇒ $3416 = P × 112/100
⇒ P × 112/100 = $3416
⇒ P = 3416/112/100
⇒ P = 3416 × 100/112
⇒ P = 3416 × 100/112
⇒ P = 341600/112
⇒ P = $3050
Thus, the sum borrowed (P) = $3050 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 3416, then the Principal = 100/112 × 3416
= 100 × 3416/112
= 341600/112
= 3050
Thus, Principal = $3050
Thus, the sum borrowed = $3050 Answer
Similar Questions
(1) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 5% simple interest?
(2) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?
(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 8% simple interest?
(4) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.
(6) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.
(8) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(9) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.