Question

You are planning for retirement 34 years from now. You plan to invest $2,100 every six months for the first seven years, $3,450 every six months for the next 11 years and $7,250 every six months for the following 16 years. If you believe you will earn an effective annual rate of return of ten percent, what will your retirement investment be worth 34 years from now? What would the value be today?

Relevant time for $2,100 part 1:

Relevant rate for everything:

Value of $2,100 part 1:

Relevant time for $2,100 part 2:

Value of $2,100 part3 2:

Relevant time for $3,450 part 1:

Value of $3,450 part 1:

Relevant time for $3,450 part 2:

Value of $3,450 part 2 :

Relevant time for $7,250:

Value of $7,250:

Total value at retirement:

Total value today:

Answer 1

Case 1: Deposit 2,100 every six months for next seven years at rate of 10%. Rate should be 5% and number of periods are 14 (7*2)

Thsi can be calculated using FV function in EXCEL

=FV(rate, nper, pmt, pv, type)

=FV(5%,14,-2100,0,0)=$41,157.13

This amount will compound at an annual interest rate of 10% for next 27 years

amount1=$41,157.13*(1+10%)^27

amount1=$539,569.70

Case 2: Deposit of 3,450 for every six months for the next 11 years.

FV(5%,22,-3450,0,0)=$132,842.99

This amount will be compunded at an annual rate of 10% for next 16 Years.

amount2=$132,842.99*(1+10%)^16=610,409.95

Case 3: Deposit 7250 for the next 16 years bi-annauly

FV(5%,32,-7250,0,0)=$545,916.51

amount3:$545,916.51

Total value at retirement=amount1+amount2+amount3=$1,695,896.16

Value at today=$1,695,896.16/(1.10)^34=$66,381.64