Question

Geometric Gradient

2.- A Self employed worker has the goal to accumulate $1,000,000 dlls. In 20 years when he retires. He has an offer of a fund that pays 8% compounded annually. He expect that his income will grow from 6 o 8% per year. He is trying to determine the size of the First Deposit A1 if his first deposit is a the end of his first year at work and the deposits grow a) 6% b) 8%

Please step by step.

Thank you!

Answer 1

Solution:

The goal is to accumulate 1000,000 dollars at the end of 20 years.

We need to find the first deposit of his at the end of first year for the both the cases i.e. if the deposit grows by 6% and in second case by 8%.

It is a problem of time value of money where we are given the future value and we need to find the payments that are to be made in 20years for each year.

1) When the deposits grow by 6%.

The future value FV = 1000,000 , N =20 , I/Y = 6% , PV=0 , PMT =?

We will use our BA II plus calculator and enter the respective values in the TVM row.

On entering the values and computing for the Payments we get the size of the deposit / first deposit is 27184.556 $

2) When the deposits grow by 8%.

The future value FV = 1000,000 , N =20 , I/Y = 8% , PV=0 , PMT =?

We will use our BA II plus calculator and enter the respective values in the TVM row.

On entering the values and computing for the Payments we get the size of the deposit / first deposit is 21852.2088 $