Question

Can I pls get some help

Answer 1

Answer:

Principal: $1,905.63

Step-by-step explanation:

Definitions:

• Simple interest is commonly used for short-term loans.

• Principal: the total amount borrowed from a lender, or deposited into a savings account.

• Interest: this is the fee that lenders charge for loaning funds, or the fee that banks pay the depositor (saver) for lending out a portion of the depositor's savings to other loaners.

• Interest rate: it is the percentage of the principal amount over a given period of time.

Simple Interest Formula:

The formula for finding the simple interest is:

A = P (1 + r × t )

Where:

A  = amount (future value) = $2,100

P  = present value of the principal = unknown

r   = annual simple interest rate  = 3.4% or 0.034

t   = time = 3 years  

Solution:

Substitute the given values into the Simple interest formula:

   ⇒    A = P (1 + r × t )

$2,100 = P (1 + [0.034 × 3] )  

$2,100 = P (1 + [0.102] )

$2,100 = P (1 .102)

Divide both sides by 1.102 to isolate "P":

$\displaystyle\mathsf{\frac{\tex\ 2,100}{1.102}\:=\:\frac{P(1.102)}{1.102}}$

P = $1,905.63

Therefore, the principal amount of investment required to reach a future value amount of $2,100 at an annual interest rate of 3.4% at the end of 3 years is $1,905.63.  

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Additional Note:

Alternatively, we can make the Principal (P) as the subject of the Simple Interest Formula:

A = P (1 + r × t )

Divide both sides by (1 + r × t ):

$\displaystyle\mathsf{\frac{A}{1+r\:\times\:t}\:=\:\frac{P(1+r\:\times\:t)}{1+r\:\times\:t}}$

$\displaystyle\mathsf{P\:=\:\frac{A}{1+r\:\times\:t}}$

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Keywords:

Simple interest

Principal

Interest rate

Present value

Future value

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Learn more about simple interest here:

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