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ami would like to withdraw $10,364.10 at the end of each year, for 10 years, from an account paying 2.3% compounded annually. Determine the amount needed in the account for Tami to do this. Round to the nearest cent.

Respuesta :

hisroyal1
Answer = $3,140.64


EXPLANATION

Given,

Amount, A = 10,364.10
Rate, r = 2.3
Number of times interest is compounded per year, n = 1
Time (in years), t = 1
Principal, P = ?

Formula: A = P [tex](1 + \frac{r}{n} )^{nt} [/tex]

10,364.10 = P [tex]( 1 + \frac{2.3}{1} )^{1} [/tex]

10,364.10 = P + 2.3P

10,364.10 = 3.3P

P = [tex] \frac{10,364.10}{3.3} [/tex]

P = 3,140.64 (Rounded off to the nearest cent)

Answer:

The amount needed in the account is $ 91,651.91 .

Step-by-step explanation:

This can be solved applying the annuity formula for a present value.

The annual withdraw is P=$10,364.10.

The interest rate is r=2.3%, compounded anually.

The period for the withdrawals is n=10 years.

The amount needed in the account is equal to the present value ot the withdrawals:

[tex]PV=\sum_{k=1}^{10} \dfrac{P}{(1+r)^k}=\dfrac{P}{r}\left[1-(1+r})^{-10}\right]\\\\\\ PV=\dfrac{10,364.10}{0.023}\left[1-(1.023})^{-10}\right]\\\\\\PV=450,613.04\left[1-0.80\right]\\\\\\PV=450,613.04*0.20\\\\\\PV= 91,651.91[/tex]

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