Question

Lauren invests $300 each month into an annuity that earns 7.1% annual interest, compounded monthly, for 35 years. She puts together the following formula to show her account balance at the end of the 35 years. A=420((1+0.071/12)^300 -1)/0.071/12.

Answer 1

The formula provided by Lauren to calculate her account balance at the end of 35 years is incorrect. The correct formula for calculating the future value of an annuity with monthly contributions can be derived using the future value of an ordinary annuity formula. The correct formula is:

A = P * ((1 + r/n)^(nt) - 1) / (r/n)

Where:

A = Account balance at the end of the 35 years

P = Monthly contribution amount ($300)

r = Annual interest rate (7.1% or 0.071)

n = Number of compounding periods per year (12, since it is compounded monthly)

t = Number of years (35)

Using the correct formula, the calculation for Lauren's account balance would be:

A = 300 * ((1 + 0.071/12)^(12*35) - 1) / (0.071/12)

Calculating this expression will give you the accurate account balance at the end of 35 years.