Question:
Andrew had to pay $5088 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
$4800
Solution And Explanation
Solution
Given,
Amount (A) = $5088
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
$5088 = P (1 + 2% × 3)
⇒ $5088 = P (1 + 2/100 × 3)
⇒ $5088 = P (1 + 2 × 3/100)
⇒ $5088 = P (1 + 6/100)
⇒ $5088 = P (100 + 6/100)
⇒ $5088 = P × 106/100
⇒ P × 106/100 = $5088
⇒ P = 5088/106/100
⇒ P = 5088 × 100/106
⇒ P = 5088 × 100/106
⇒ P = 508800/106
⇒ P = $4800
Thus, the sum borrowed (P) = $4800 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 5088, then the Principal = 100/106 × 5088
= 100 × 5088/106
= 508800/106
= 4800
Thus, Principal = $4800
Thus, the sum borrowed = $4800 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?
(2) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(3) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 4 years.
(5) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?
(6) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 3 years.
(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?
(9) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 7 years.