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) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(2) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?
(3) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(4) What amount does James have to pay after 6 years if he takes a loan of $3000 at 3% simple interest?
(5) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 7 years.
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.
(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.
(9) Karen had to pay $4305.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.