On part 4: 12,849.00 is the required present value.
In bank statement format, looks like:
Need anything else on that one?Code:YEAR PAYMENT INTEREST BALANCE 0 12849.00 1 -1000.00 1284.90 13133.90 2 -1057.69 1313.39 13389.60 3 -1118.71 1338.96 13609.85 ... 18 -2594.82 680.81 4894.07 19 -2744.52 489.41 2638.96 20 -2902.85 263.89 .00
Sorry, thought you meant question #4...
Your problem states: "for a rate of interest of 6% per annum
effective, calculate the following equivalent rates".
6% effective means 100 is worth 106 after 1 year,
no matter how often the interest is paid.
An equivalent rate is calculated and used to achieve
this; as example, 1.467% per quarter.
Please explain what you mean by "equivalent".
Also, what is the difference between "rate of interest"
and "rate of discount"?
Look at it as 2 bank accounts:
one in which the payments are deposited
one where the initial amount is deposited
Their values in 20 years must equal each other: OK?
i = .10 (annual rate)
j = .057692 (payment annual increase)
n = 20 (number of years)
f = 1000 (first payment)
p = present (or purchase) value (?)
u = future value of p (?)
v = future value of payments (?)
u = p(1+i)^n
v = f[(1+i)^n - (1+j)^n] / [(1+i) - (1+j)]
Since u = v:
p = v / (1+i)^n
Substitute the values in there: result will be p = 12849.005132....