Question:
Steven had to pay $5152 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
$4600
Solution And Explanation
Solution
Given,
Amount (A) = $5152
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
$5152 = P (1 + 4% × 3)
⇒ $5152 = P (1 + 4/100 × 3)
⇒ $5152 = P (1 + 4 × 3/100)
⇒ $5152 = P (1 + 12/100)
⇒ $5152 = P (100 + 12/100)
⇒ $5152 = P × 112/100
⇒ P × 112/100 = $5152
⇒ P = 5152/112/100
⇒ P = 5152 × 100/112
⇒ P = 5152 × 100/112
⇒ P = 515200/112
⇒ P = $4600
Thus, the sum borrowed (P) = $4600 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 5152, then the Principal = 100/112 × 5152
= 100 × 5152/112
= 515200/112
= 4600
Thus, Principal = $4600
Thus, the sum borrowed = $4600 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(2) Margaret had to pay $4741.5 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 after 10 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(4) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
(5) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 2% simple interest?
(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.
(7) How much loan did Barbara borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6937.5 to clear it?
(8) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8344 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.
(10) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.