Question:
Mary had to pay $3233 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
$3050
Solution And Explanation
Solution
Given,
Amount (A) = $3233
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
$3233 = P (1 + 2% × 3)
⇒ $3233 = P (1 + 2/100 × 3)
⇒ $3233 = P (1 + 2 × 3/100)
⇒ $3233 = P (1 + 6/100)
⇒ $3233 = P (100 + 6/100)
⇒ $3233 = P × 106/100
⇒ P × 106/100 = $3233
⇒ P = 3233/106/100
⇒ P = 3233 × 100/106
⇒ P = 3233 × 100/106
⇒ P = 323300/106
⇒ P = $3050
Thus, the sum borrowed (P) = $3050 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 3233, then the Principal = 100/106 × 3233
= 100 × 3233/106
= 323300/106
= 3050
Thus, Principal = $3050
Thus, the sum borrowed = $3050 Answer
Similar Questions
(1) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.
(3) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.
(4) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 10% simple interest?
(5) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 7% simple interest?
(6) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(7) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 3 years.
(9) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?
(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.