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Interest-only loans and perpetuities

Question 1 of 8

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A regional arts fund has the cash-flow conditions below

Let $V_n$ be the balance, in dollars, after $n$ periods and before the next period's interest is applied. Interest is applied first and the cash flow occurs at the end of each period

The initial principal is $603,105. The nominal annual rate is 3%, compounded annually. The equal end-of-year cash flow D is to be determined

This is a perpetuity income model. The fund pays the cash flow to the investor after interest is added, and the fund balance is the amount retained

V_{n+1}=RV_n+sD

For part (a), compare a proposed cash flow of $18,093.15 per year with one period's interest. The proposed amount is used only for that comparison; the recurrence uses D

(a)1 mark

Decide whether the fund balance grows, falls or stays constant with the proposed amount

The fund balance grows because the proposed income payment of $18,093.15 is below the interest on the balance, $18,093.15

The fund balance falls because the proposed income payment of $18,093.15 is above the interest on the balance, $18,093.15

The fund balance stays constant because the proposed income payment of $18,093.15 equals the interest on the balance, $18,093.15

(b)4 marks

Fill the initial value, period multiplier, cash-flow sign and cash-flow magnitude for the model

Starting balance V₀ ($) Period multiplier R Sign s Cash-flow amount D ($)

What periodic income payment keeps the fund balance unchanged after each year? Give the answer to the nearest cent

Periodic payment ($) Format: nearest cent