Annuity Account Precalculus Future Value

Question

You just graduated from college and want to set up a fund for your future needs. You decide to invest $150 weekly in an annuity account, at an annual rate of 8.5% compounded weekly. If you are now 22 years old, what will the account value be in 33 years when you are 55?

Answer 1

The formula for the Future Value of an Ordinary Annuity, has the following formula:

 

NOTE:  Pre-Suppose that the decimal carry-out of 0.085/52.5 is:  0.00161905

 

FV_A = PMT [1 + (0.085/52.5)^{33 * 52.5} -1] / (0.085/52.5)]

 

FV_A = 150 * [1 + (0.085/52.5)^1732.5 -1] / [(0.085/52.5)]

 

FV_A = 150 * $1,435,066.61

 

When calculated on the HP 12C, to 8 decimal places, get:  $1,433,833.49

 

The accepted answer depends upon whether instructor insists upon use of tables, # of decimal places rounded to during the calculation, etc.