please help

Keith started saving for retirement at age 45 with plans to retire at age 70. He invested an average of $500 per month in various securities, with an average annual return of 6% adjusted for inflation. Assuming monthly compounding, how much has Keith saved at the start of retirement?

$27,432.26

$446,496.98

$346,496.98

$712,355.15

Question

please help

 Keith started saving for retirement at age 45 with plans to retire at age 70. He invested an average of $500 per month in various securities, with an average annual return of 6% adjusted for inflation. Assuming monthly compounding, how much has Keith saved at the start of retirement?

$27,432.26

$446,496.98

$346,496.98

$712,355.15

anonymous · Answer

@amistre64

anonymous · Answer

can you explain!

mathstudent55 · Answer

$ FV = A \times \dfrac {(1 + i)^n - 1}{i} $

FV = future value
n = number of periods
i = interest rate per period as a decimal
A = annualized (monthly) payment

mathstudent55 · Answer

$ FV = A \times \dfrac {(1 + i)^n - 1}{i}$

$n = 25 \times 12$ = 300

$i = \dfrac {6}{12 \times 100} = 0.005$


$ FV = $500 \times \dfrac {(1 + 0.005)^{300} - 1}{0.005} $

$FV = $346,496.98 $

Choice C.