How much to deposit today

[brunettie91]

I have no idea how to do this one...

The amount a person would need to deposit today to be able to withdraw $6000 each year for 10 years from an account earning 6% interest.

I have a chart with all the compounding interest..I just don't know how to start the equation or what equation to use

 

[soroban]

Hello, brunettie91!

This is more involved than Compound Interest.

The amount a person would need to deposit today to be able to withdraw $6000 each year
for 10 years from an account earning 6% interest.

Amortization Formula: .\(\displaystyle A \;=\;P\dfrac{i(1+i)^n}{(1+i)^n-1}\)

. . where: .\(\displaystyle \begin{Bmatrix}A &=&\text{periodic payment} \\ P &=& \text{principal borrowed} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \end{Bmatrix}\)


Consider that you borrowed \(\displaystyle P\) dollars.
The loan charges 6% interest annualy.
You will repay the loan with annual payments of $6000 each for ten years.
How much can you borrow?

We have: .\(\displaystyle \begin{pmatrix}A &=& 6000 \\ i &=& 0.06 \\ n &=& 10\end{pmatrix}\)

Substitute: .\(\displaystyle 6000 \:=\\dfrac{(0.06)(1.06)^{10}}{(1.06)^{10} - 1} \quad\Rightarrow\quad 6000 \:=\(0.135867958)\)

Hence: .\(\displaystyle P \;=\;\dfrac{6000}{0.135867958} \;=\;44,\!160.52231 \)


Therefore: .\(\displaystyle P \;\approx\;\$44,160.52\)