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Analyse a cash-flow model with changed conditions

Question 1 of 8

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The business reserve account is modelled with a periodic cash flow and a change in conditions

$V_0$ is the initial reserve balance, before interest or a cash flow. Here $V_0$=$198,000. Every cash flow is made at the end of its period, after interest

The stage-one nominal annual rate is 10%, compounded annually. The one-period rate is 10%, so the multiplier is $R_1=11/10$

An addition of $318 is made at the end of each year, after interest

After 5 periods, the regular cash flow changes from $318 to $374. The nominal annual rate remains 10%

The stage-two nominal annual rate is 10%, compounded annually. The one-period rate is 10%, so the multiplier is $R_2=11/10$

An addition of $374 is made at the end of each year, after interest

The second stage lasts for 3 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

What is the balance when the first stage ends? Give the answer to the nearest cent

Stage-one balance ($) Format: nearest cent

(b)3 marks

Record the quantities needed for the second-stage recurrence. 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

What is the final value of the model? Give the answer to the nearest cent

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