1 of 8 0-day streak

Interest-only loans and perpetuities

Question 1 of 8

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Consider the sporting association fund

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 $69,576. The nominal annual rate is 10.5%, 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 $8,766.57 per year with one period's interest. The proposed amount is used only for that comparison; the recurrence uses D

(a)1 mark

What happens to the fund balance after each year if the proposed cash flow is used?

The fund balance falls after each period because the proposed cash flow of $8,766.57 is above one period's interest of $7,305.48

The fund balance grows after each period because the proposed cash flow of $8,766.57 is below one period's interest of $7,305.48

The fund balance stays constant after each period because the proposed cash flow of $8,766.57 equals one period's interest of $7,305.48

(b)4 marks

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

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

Find the end-of-year amount that preserves the starting fund balance. Give the answer to the nearest cent

Periodic payment ($) Format: nearest cent