Question

You want to retire exactly 40 years from today with $1,970,000 in your retirement account. If you think you can earn an interest rate of 10.15 percent compounded monthly, how much must you deposit each month to fund your retirement

Answer 1

Answer:

I must deposit $297.59 each month

Explanation:

Future Value

A series of deposits of R dollars each for n periods at an interest rate i will generate a final value M, given by

$M=F_m\cdot R$

Where Fm is computed by

$\displaystyle F_m=\frac{(1+i)^n-1}{i}$

The question provides us with the values

i=10.15% , n=40 years

Converting to monthly periods

$\displaystyle i=\frac{10.15}{100\cdot 12}=0.00846$

$n=40\cdot 12=480$

Therefore

$\displaystyle F_m=\frac{(1+0.00846)^{480}-1}{0.00846}=6,619.84$

Solving the first equation for R

$\displaystyle R=\frac{FV}{F_m}=\frac{1,970,000}{6,619.84}=297.59$

R=$297.59