Question

Suppose your starting salary is $70,000 per year. You deposit 10% each year in a savings account that earns 6% interest. Your salary increases by 5% per year, and inflation is 3% per year. How much do you have in your savings account after 40 years? What is that worth in today's dollars? g

Answer 1

Answer:

Instructions are listed below.

Explanation:

Giving the following information:

Suppose your starting salary is $70,000 per year. You deposit 10% each year in a savings account that earns 6% interest. Your salary increases by 5% per year, and inflation is 3% per year.

The interest rate and the growth rate of the salary will increase the future value of the deposits. On the contrary, the inflation rate will decrease the real purchasing power of money.

To simplify the calculation, we will include the growth effect and the inflation rate to the interest rate:

Real interest rate= 0.06 + 0.05 - 0.03= 0.08

Now, using the following formula, we can calculate the final value:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit= 70,000

i= 0.08

n= 40

FV= {70,000*[(1.08^40)-1]}/ 0.08

FV= $18,133,956.31

Finally, we calculate the present value:

PV= FV/(1+i)^n

PV= 18,133,956.31/ (1.08^40)

PV= 834,722.93