Question

In trying to apply my knowledge in the real world, I am trying to create a realistic retirement schedule. However, I am running into difficulties using both a financial calculator as well as our equations from class in doing this.

I am trying to do the following: plan a retirement schedule between the ages of 25 and 70, in which I would deposit 20% of my income each year. The income starts at 80,000 with an annual growth rate of 4% and, to be realistic, assuming an interest rate of 2.5%. I will assume for simplicity that I receive my first salary ($80,000) when I turn 25, and my last salary when I turn 70. As soon as I receive a salary, I will save 20% of it.

I would like to know (1) how much I will have in my retirement account when I turn 70, immediately after the last deposit, and (2) what single deposit made on my 25^th birthday would give the same account balance when I turn 70.

However, this raises issues, as if I try to use the equation for the present value of a growing annuity with a 4% growth rate and 2.5% discount rate, r-g will yield a negative number. Also, I could not find online how to do this on my HP 10bII+ financial calculator and I don't want to manually enter 46 payments.

Do you know how I could overcome this obstacle?

All the best,

Jimmy

Unfortunately, I forgot to reply Jimmy’s email and I would like to get back to him as soon as possible. I want to answer Jimmy’s questions using the formulas we learned in class (not the calculator or Excel). You may use the calculator or Excel for calculations, but I want to send Jimmy the formula solution. Can you help me draft a response?

1. Briefly comment on Jimmy’s concern that “if I try to use the equation for the present value of a growing annuity with a 4% growth rate and 2.5% discount rate, r-g will yield a negative number”. (3 sentences at most) Please show by hand(without calculator or excel)
2. How much will Jimmy have in his retirement account when he turns 70, immediately after the last deposit? Please show by hand(without calculator or excel)
3. What single deposit made on Jimmy’s 25^th birthday would give the same account balance when he turns 70? Please show by hand(without calculator or excel)

Answer 1

Please check the solution attached.
Date : MON TUE WED THU FRI SAT SUN OOOOOOO m 28 0 25 26 27 Let say ^ Amount deposited posited at 28th year at 25th year 26th year 27th = = = x A A x Cl-ou) AXC1:04) le 70th year = Ax(1.04) Duration for amount deposited on 28th year = us years 26th year = 44 70th year : 0 years 1.025149 Amount deposited at 25th year will become a AX 1.025 aft on maturity Il - 26 AX1.04 x 1025^ 023144 10 us 20 us 20 - Ax 1.04 x 1.025 A (m-N+) L ( 4) A t1onst 4*1.025 2x10025 - Formula = AX U I thyet) whue A = 200 x 80000 =16000 Hledy I 1.025