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Analyse a cash-flow model with changed conditions

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The retirement income account is modelled with a periodic cash flow and a change in conditions

$V_0$ is the initial account balance, before interest or a cash flow. Here $V_0$=$64,250. Every cash flow is made at the end of its period, after interest

The stage-one nominal annual rate is 5%, compounded annually. The one-period rate is 5%, so the multiplier is $R_1=21/20$

A withdrawal of $5,916.50 is made at the end of each year, after interest

After 3 periods, the regular cash flow changes from $5,916.50 to $4,750.50. The nominal annual rate remains 5%

The stage-two nominal annual rate is 5%, compounded annually. The one-period rate is 5%, so the multiplier is $R_2=21/20$

A withdrawal of $4,750.50 is made at the end of each year, after interest

The second stage lasts for 2 years

This is an exact-carry recurrence: keep full precision within and between both stages. Round only each requested displayed result. The model has no fees or other transactions

(a)1 mark

Find the balance immediately before the conditions change, after 3 years. Give the answer to the nearest cent

Stage-one balance ($) Format: nearest cent

(b)3 marks

Set up the recurrence for the periods after the change. Use the exact stage-one balance as the starting value; do not feed its displayed rounding into stage two

V_{k+j+1}=R_2V_{k+j}+s_2D_2

Use exact values in the setup table; fractions are allowed
Stage-two field	Value
Starting balance V_k	exact stage-one balance
Stage-two period multiplier R_2	?
Signed stage-two cash flow sD_2	?
Number of stage-two periods	?

Stage-two period multiplier R_2 Signed stage-two cash flow sD_2 Number of stage-two periods

Find the balance at the end of the second stage. Give the answer to the nearest cent

Stage-two final balance ($) Format: nearest cent