Question:
Michelle had to pay $5247 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
$4950
Solution And Explanation
Solution
Given,
Amount (A) = $5247
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
$5247 = P (1 + 2% × 3)
⇒ $5247 = P (1 + 2/100 × 3)
⇒ $5247 = P (1 + 2 × 3/100)
⇒ $5247 = P (1 + 6/100)
⇒ $5247 = P (100 + 6/100)
⇒ $5247 = P × 106/100
⇒ P × 106/100 = $5247
⇒ P = 5247/106/100
⇒ P = 5247 × 100/106
⇒ P = 5247 × 100/106
⇒ P = 524700/106
⇒ P = $4950
Thus, the sum borrowed (P) = $4950 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 5247, then the Principal = 100/106 × 5247
= 100 × 5247/106
= 524700/106
= 4950
Thus, Principal = $4950
Thus, the sum borrowed = $4950 Answer
Similar Questions
(1) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 3 years.
(2) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.
(4) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 3% simple interest?
(5) Elizabeth had to pay $3760.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 5% simple interest?
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.
(8) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(10) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 7 years.