Starting at age 32 you put 600 at the end of each quarter in

Starting at age 32, you put $600 at the end of each quarter into an account paying 2. 1% compounded quarterly. At age 45, you withdraw the entire amount and place it into a new account that pays 3.6% compounded monthly. From then on, you deposit $490 per month into this account. How much will you have for retirement at age 65?

Solution

Futire Value of regualr payment of $600 every quarter:

C = $600 ; i = 0.021/4 ; n = 4*13 = 52

FV = C[ (1+i)^n -1]/i

= 600[ (1.00525^52 -1]/0.00525 = $ 35767.12

Now this amt is deposied at 3.6%comunded monthly along with regualr payment of $490

rate = 3.6% ; i = 0.036/12 =0.003 ; n = 12*20 = 240

Amount = Pricipal[ 1+ 0.003]^240 + C[(1+i)^n -1]/i

=  35767.12[1.003]^240 + 490[1.003^240 -1]/0.003

= $ 73402 + $171862.60

= $245264.60 at the time of retirement of age 65