Question:
( 1 of 10 ) Jessica had to pay $3975 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(A) 4 47/50 Or, 247/50
(B) 8 47/50 Or, 447/50
(C) 4 141/50 Or, 341/50
(D) 4 94/50 Or, 294/50
You selected
$2981.25
Correct Answer
$3750
Solution And Explanation
Solution
Given,
Amount (A) = $3975
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
$3975 = P (1 + 2% × 3)
⇒ $3975 = P (1 + 2/100 × 3)
⇒ $3975 = P (1 + 2 × 3/100)
⇒ $3975 = P (1 + 6/100)
⇒ $3975 = P (100 + 6/100)
⇒ $3975 = P × 106/100
⇒ P × 106/100 = $3975
⇒ P = 3975/106/100
⇒ P = 3975 × 100/106
⇒ P = 3975 × 100/106
⇒ P = 397500/106
⇒ P = $3750
Thus, the sum borrowed (P) = $3750 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 3975, then the Principal = 100/106 × 3975
= 100 × 3975/106
= 397500/106
= 3750
Thus, Principal = $3750
Thus, the sum borrowed = $3750 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) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.
(3) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.
(5) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(6) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?
(7) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(9) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 8% simple interest?
(10) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?