Question:
Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
Correct Answer
$4100
Solution And Explanation
Solution
Given,
Amount (A) = $4346
Rate of Simple Interest (R) = 2%
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
$4346 = P (1 + 2% × 3)
⇒ $4346 = P (1 + 2/100 × 3)
⇒ $4346 = P (1 + 2 × 3/100)
⇒ $4346 = P (1 + 6/100)
⇒ $4346 = P (100 + 6/100)
⇒ $4346 = P × 106/100
⇒ P × 106/100 = $4346
⇒ P = 4346/106/100
⇒ P = 4346 × 100/106
⇒ P = 4346 × 100/106
⇒ P = 434600/106
⇒ P = $4100
Thus, the sum borrowed (P) = $4100 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 6
Thus, simple interest for 3 years = 6
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 6 = 106
Calculation of the Principal
Now,
∵ If the Amount is 106, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/106
∴ If the Amount is 4346, then the Principal = 100/106 × 4346
= 100 × 4346/106
= 434600/106
= 4100
Thus, Principal = $4100
Thus, the sum borrowed = $4100 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(2) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 to clear the loan, then find the time period of the loan.
(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 3% simple interest?
(4) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?
(5) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 3 years.
(7) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 3 years.
(9) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 8% simple interest?
(10) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.