Question

Slim made a single deposit of $5,000 in an account that pays 7.2% in 2015. What equal-sized annual withdrawals can Slim make from the account if the first withdrawal occurs in 2020 and the last occurs in 2025

Answer 1

Answer:

annual withdrawals is  $1,393.87

Explanation:

given data

Amount Deposited = $5,000

Annual Interest Rate = 7.2%

First withdrawal =  2020

last withdrawal = 2025

solution

we consider equal sized annual withdrawals = x

so we can say that Amount Deposited amount will be as

$5,000 = $\frac{x}{(1+0.72)^5} + \frac{x}{(1+0.72)^6} + \frac{x}{(1+0.72)^7} + \frac{x}{(1+0.72)^8} + \frac{x}{(1+0.72)^9} + \frac{x}{(1+0.72)^{10}}$       ..........1

we take common here $\frac{x}{(1+0.72)^{4}}$

so

$5,000 = $\frac{x}{(1+0.72)^{4}} \times ( \frac{1}{(1+0.72)^1} + \frac{1}{(1+0.72)^2} + \frac{1}{(1+0.72)^3} + \frac{1}{(1+0.72)^4} + \frac{1}{(1+0.72)^5} + \frac{1}{(1+0.72)^{6}} )$      

solve it we get

x = $1,393.87  

so that annual withdrawals is  $1,393.87