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Interest-only loans and perpetuities

Question 1 of 8

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The regional hospital fund is modelled over equal year periods

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 $832,129. 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 $18,722.91 per year with one period's interest. The proposed amount is used only for that comparison; the recurrence uses D

(a)1 mark

Which statement describes the direction of the fund balance under the proposed cash flow?

The proposed income payment gives a fund balance that falls. The proposed amount is $18,722.91, and the one-period interest is $24,963.87; the amount is above the interest

The proposed income payment gives a fund balance that grows. The proposed amount is $18,722.91, and the one-period interest is $24,963.87; the amount is below the interest

The proposed income payment gives a fund balance that stays constant. The proposed amount is $18,722.91, and the one-period interest is $24,963.87; the amount equals the interest

(b)4 marks

Record the four quantities in the recurrence template $V_{n+1}=RV_n+sD$

$P\ (\$)$ $R=1+r_p$ $s$ $D\ (\$)$

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

Periodic payment ($) Format: nearest cent