1 of 8 0-day streak

Interest-only loans and perpetuities

Question 1 of 8

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Use the following end-of-year model for the university support 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 $370,562. 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 $46,690.81 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 grows. The proposed amount is $46,690.81, and the one-period interest is $38,909.01; the amount is below the interest

The proposed income payment gives a fund balance that falls. The proposed amount is $46,690.81, and the one-period interest is $38,909.01; the amount is above the interest

The proposed income payment gives a fund balance that stays constant. The proposed amount is $46,690.81, and the one-period interest is $38,909.01; the amount equals the interest

(b)4 marks

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

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

Determine the income payment D for the same balance after every year. Give the answer in dollars to the nearest cent

Periodic payment ($) Format: nearest cent