Question

You want to be able to withdraw $30,000 each year for 25 years. Your account earns 8% interest compounded annually.

a. How much do you need in your account at the beginning?

b. How much total money will you pull out of the account?

c. How much of that money is int

Answer 1

Answer:

amount is $320243.25 need in your account at the beginning

Money pull in 25 years is $750000

money interest is $429756.75

Step-by-step explanation:

Given data

principal (P) = $30000

time (t) = 25 years

rate (r) = 8% = 0.08

to find out

amount need in beginning, money pull out , and interest money

solution

We know interest compounded annually so n = 1

we apply here compound annually formula i.e.

amount = principal ( 1 - $(1+r/n)^{-t}$ / r/k

now put all these value principal, r , n and t in equation 1

amount = 30000 ( 1 - $(1+0.08/1)^{-25}$ / 0.08/1

amount = 30000 × 0.853982  / 0.08

amount = $320243.25 need in your account at the beginning

Money pull in 25 years is $30000 × 25 i.e

Money pull in 25 years is $750000

money interest = total money pull out in 25 years - amount at beginning need

money interest = $750000 - $320243.25

money interest = $429756.75

Answer 2

The cash flow in the account are;

a. Amount in the account at the beginning is approximately $320,243.3

b. The total money pulled out is $750,000

c. Amount of in interest in money pulled out approximately $429,756.7

The reason the above values are correct are as follows;

The given parameter are;

The amount to be withdrawn each year, d = $30,000

The number of years of withdrawal, n = 25 years

The interest rate on the account = 8 %

a. The amount that should be in the account at the beginning is given by the payout annuity formula as follows;

$P_0 = \dfrac{d \times \left(1 - \left(1 + \dfrac{r}{k} \right)^{-n\cdot k}\right) }{\left(\dfrac{r}{k} \right)}$

P₀ = The principal or initial balance in the account at the beginning

d = The amount to be withdrawn each year = $30,000

r =  The interest rate per annum = 8%

k = The number of periods the interest is applied in a year = 1

n = The number of years withdrawal is made = 25

We get;

$P_0 = \dfrac{30,000 \times \left(1 - \left(1 + \dfrac{0.08}{1} \right)^{-25\times 1} \right) }{\left( \dfrac{0.08}{1} \right)} \approx 320,243.3$

The amount needed in the account at the beginning, P₀ ≈ $320,243.3

b. The amount of money pulled out, A = n × d

Therefore, A = 25 × $30,000 = $750,000

c. The amount of money received as interest, I = A - P₀

∴ I = $750,000 - $320,243.3 ≈ $429,756.7

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