Question

Find the present value given the following: Amount needed: $12,300Time in years: 4Interest: 6%Compounded: Annually

Answer 1

Given:

Amount needed = $12,300

Time = 4 years

Interest = 6% ==> 0.06

Compounded annually.

Let's find the present value.

To find the present value, apply the compounded interest formula:

$A=P(1+r)^t$

Where:

A is the amount needed = $12,300

r is the interest rate = 0.06

t is the time = 4 years

P is the principa or the present value.

Ipput values into the formula and solve for P.

We have:

$\begin{gathered} 12300=P(1+0.06)^4 \\ \\ 12300=P(1.06)^4 \\ \\ 12300=P(1.26245) \end{gathered}$

Divide both sides by 1.26245:

$\begin{gathered} \frac{12300}{1.26245}=\frac{P(1.26245)}{1.26245} \\ \\ 9742.75=P \\ \\ P=9742.75 \end{gathered}$

Therefore, the present value is $9742.75

ANSWER:

$9742.75