Question

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.

Answer 1

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
`(1 + (r)/(n) )^(nt)`

10,364.10 = P
`( 1 + (2.3)/(1) )^(1)`

10,364.10 = P + 2.3P

10,364.10 = 3.3P

P =
`(10,364.10)/(3.3)`

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

Answer 2

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

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:

`PV=\sum_(k=1)^(10) (P)/((1+r)^k)=(P)/(r)\left[1-(1+r})^(-10)\right]\\\\\\ PV=(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`