Question:
Matthew had to pay $4704 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
$4200
Solution And Explanation
Solution
Given,
Amount (A) = $4704
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
$4704 = P (1 + 4% × 3)
⇒ $4704 = P (1 + 4/100 × 3)
⇒ $4704 = P (1 + 4 × 3/100)
⇒ $4704 = P (1 + 12/100)
⇒ $4704 = P (100 + 12/100)
⇒ $4704 = P × 112/100
⇒ P × 112/100 = $4704
⇒ P = 4704/112/100
⇒ P = 4704 × 100/112
⇒ P = 4704 × 100/112
⇒ P = 470400/112
⇒ P = $4200
Thus, the sum borrowed (P) = $4200 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 4704, then the Principal = 100/112 × 4704
= 100 × 4704/112
= 470400/112
= 4200
Thus, Principal = $4200
Thus, the sum borrowed = $4200 Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.
(2) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 8 years.
(3) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.
(4) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(5) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?
(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.
(8) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(10) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.