Question:
Donna had to pay $5432 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
$4850
Solution And Explanation
Solution
Given,
Amount (A) = $5432
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
$5432 = P (1 + 4% × 3)
⇒ $5432 = P (1 + 4/100 × 3)
⇒ $5432 = P (1 + 4 × 3/100)
⇒ $5432 = P (1 + 12/100)
⇒ $5432 = P (100 + 12/100)
⇒ $5432 = P × 112/100
⇒ P × 112/100 = $5432
⇒ P = 5432/112/100
⇒ P = 5432 × 100/112
⇒ P = 5432 × 100/112
⇒ P = 543200/112
⇒ P = $4850
Thus, the sum borrowed (P) = $4850 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 5432, then the Principal = 100/112 × 5432
= 100 × 5432/112
= 543200/112
= 4850
Thus, Principal = $4850
Thus, the sum borrowed = $4850 Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 4 years.
(2) Andrew had to pay $5232 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 4 years.
(4) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(5) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?
(7) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.
(9) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?
(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 7 years.