Question

QUESTION 17 Starting next month, if you make monthly deposits of $619 into a retirement account that earns 6% interest compounded monthly, how large will your retirement account be in 33 years? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Answer 1

Future value at the end of year 33 = fv = pmtx ((1+r)^n-1))/ $768,438.79 [$619*(((1.0054396)-1)/0.005)]

Answer 2

SOLUTION ;

Monthly compounding.

First deposit stars from next month. So, ordinary annuity case.

Monthly deposit, A = 619 ($)

Monthly interest rate , r = 6/12 % = 6/1200 = 0.005  in decimals.

=> 1 + r = 1 + 0.005 = 1.005

Monthly periods, n = 33 * 12 = 396months.

So,

Amount in the account after 33 years (396 months) as per ordinary annuity formula :

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

= 619((1.005^396 - 1) / 0.005

= 768438.79 ($) (ANSWER).