Question

I currently have $45,000 saved in my retirement account. My employer-sponsored retirement plan pays me $2,250 every month, which is deposited into the same retirement account. If I am currently 25 years old and I plan to retire at age 67, what will the future value of my retirement account be after 42 years? Assume a 7.75% annual return, compounded monthly.

Answer 1

The future value of your retirement account after 42 years, assuming a 7.75% annual return compounded monthly, would be approximately $1,178,577.

To calculate the future value of your retirement account, you can use the compound interest formula:

FV = P(1 + r/n)ⁿᵗ

where:

FV is the future value of the investment/loan,

P is the principal investment amount (initial deposit or loan amount),

r is the annual interest rate (as a decimal),

n is the number of times that interest is compounded per unit t,

t is the time the money is invested/borrowed for in years.

In this case:

P = $45,000 (initial savings),

r = 7.75% or 0.0775 (annual return as a decimal),

n = 12 (compounded monthly),

t = 42 years.

Thus we have;

FV = $45,000(1 + 0.0775/12)¹²⁽⁴²⁾

FV = $45,000(1 + 0.0065)⁵⁰⁴

FV = $45,000(1.0065)⁵⁰⁴

FV = $45,000 × 26.1996

FV = $1,178,577.

Therefore, the future value of your retirement account after 42 years, considering monthly contributions and compounding interest at a rate of 7.75%, is approximately $1,178,577.