Question:
Margaret had to pay $4872 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
$4350
Solution And Explanation
Solution
Given,
Amount (A) = $4872
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
$4872 = P (1 + 4% × 3)
⇒ $4872 = P (1 + 4/100 × 3)
⇒ $4872 = P (1 + 4 × 3/100)
⇒ $4872 = P (1 + 12/100)
⇒ $4872 = P (100 + 12/100)
⇒ $4872 = P × 112/100
⇒ P × 112/100 = $4872
⇒ P = 4872/112/100
⇒ P = 4872 × 100/112
⇒ P = 4872 × 100/112
⇒ P = 487200/112
⇒ P = $4350
Thus, the sum borrowed (P) = $4350 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 4872, then the Principal = 100/112 × 4872
= 100 × 4872/112
= 487200/112
= 4350
Thus, Principal = $4350
Thus, the sum borrowed = $4350 Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.
(4) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 10% simple interest?
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.
(6) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 7% simple interest?
(7) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(8) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 6% simple interest?
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 4 years.
(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 7 years.