Question:
Daniel had to pay $4469 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
Correct Answer
$4100
Solution And Explanation
Solution
Given,
Amount (A) = $4469
Rate of Simple Interest (R) = 3%
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
$4469 = P (1 + 3% × 3)
⇒ $4469 = P (1 + 3/100 × 3)
⇒ $4469 = P (1 + 3 × 3/100)
⇒ $4469 = P (1 + 9/100)
⇒ $4469 = P (100 + 9/100)
⇒ $4469 = P × 109/100
⇒ P × 109/100 = $4469
⇒ P = 4469/109/100
⇒ P = 4469 × 100/109
⇒ P = 4469 × 100/109
⇒ P = 446900/109
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 4469, then the Principal = 100/109 × 4469
= 100 × 4469/109
= 446900/109
= 4100
Thus, Principal = $4100
Thus, the sum borrowed = $4100 Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?
(3) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8791 to clear the loan, then find the time period of the loan.
(4) How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?
(5) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(6) John had to pay $3584 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Emily had to pay $5035 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?
(9) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10430 to clear the loan, then find the time period of the loan.
(10) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.