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) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.
(2) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?
(3) What amount does William have to pay after 6 years if he takes a loan of $3500 at 4% simple interest?
(4) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 8% simple interest?
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.
(6) Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.
(8) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?
(10) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.