Read the financial parameters out of a linear recurrence relation

V₀ = 4000 and Vₙ₊₁ = Vₙ − 200, where n counts years. What does 200 mean?

Keep the yearly amount at $200 and change the starting value. Then keep the start at $4,000 and change the amount. Compare the resulting rate. Non-terminating results are displayed rounded to 2 decimal places

What rate does a $200 yearly amount represent on a $4,000 start?

Recover a rate

Divide the positive yearly amount by the original value and multiply by 100. Use the recurrence sign separately to decide whether the model grows or decays

1. 1Start V₀ gives the original amount
2. 2Amount D is the positive dollar amount added or subtracted each year
3. 3Rate r is the percentage number. Use the original value as the denominator \(\displaystyle r=100D/V_0\)

Initial value

\(\displaystyle V_0=4000\)

Recurrence

\(\displaystyle V_{n+1}=V_n-200\)

Read the initial value

Given values

\(\displaystyle V_{n+1}=V_n-200\)

Read the positive amount lost each year

Starting value and yearly loss

\(\displaystyle V_0=4000,\quad D=200\)

Express the yearly loss as a percentage of the starting value. Give a whole-number percentage

Given values

\(\displaystyle V_0=4000,\quad V_{n+1}=V_n-200\)

Find the value after three years

A value starts at $4,000 and increases by $200 each year. Which description fits?

Starting value and yearly increase

\(\displaystyle V_0=4000,\quad D=150\)

A $4,000 investment increases by $150 each year under simple interest. Find the annual rate to 2 decimal places

Describe the whole model

State the start, direction, amount and period in words. A yearly recurrence is not a monthly one

1. 1Example The investment starts at $4,000 and adds $150 each year, equivalent to 3.75% simple interest per year
2. 2Check separately Practise describing the start, direction, amount and period on paper