Question:
( 1 of 10 ) Joseph had to pay $3922 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
$2941.5
Correct Answer
$3700
Solution And Explanation
Solution
Given,
Amount (A) = $3922
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
$3922 = P (1 + 2% × 3)
⇒ $3922 = P (1 + 2/100 × 3)
⇒ $3922 = P (1 + 2 × 3/100)
⇒ $3922 = P (1 + 6/100)
⇒ $3922 = P (100 + 6/100)
⇒ $3922 = P × 106/100
⇒ P × 106/100 = $3922
⇒ P = 3922/106/100
⇒ P = 3922 × 100/106
⇒ P = 3922 × 100/106
⇒ P = 392200/106
⇒ P = $3700
Thus, the sum borrowed (P) = $3700 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 3922, then the Principal = 100/106 × 3922
= 100 × 3922/106
= 392200/106
= 3700
Thus, Principal = $3700
Thus, the sum borrowed = $3700 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.
(2) What amount does William have to pay after 6 years if he takes a loan of $3500 at 2% simple interest?
(3) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.
(4) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
(6) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 3 years.
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 7 years.
(9) How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?
(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.