FM FM Annuities and Loan Amortization 3

Question 1

A deferred annuity-immediate pays $1,000 per year for 10 years, with the first payment occurring at the end of year 5. At 7% annual effective interest, the present value today is approximately:

Accepted Answer

$5,358

Answer

$7,024

Answer

$6,515

Answer

$4,876

Question 2

For an annuity-due of n payments of 1 per period at interest rate i, the relationship between ä(n,i) and a(n,i) is:

Accepted Answer

ä(n,i) = a(n,i) × (1+i)

Answer

ä(n,i) = a(n,i) / (1+i)

Answer

ä(n,i) = a(n,i) + 1

Answer

ä(n,i) = a(n,i) - v^n

Question 3

An arithmetic increasing annuity-immediate has payments of $100, $200, $300, $400, $500 at the end of years 1 through 5. Which expression gives its present value at 5% annual interest?

Accepted Answer

100 × (Ia)(5, 5%)

Answer

100 × a(5, 5%)

Answer

100 × s(5, 5%)

Answer

100 × ä(5, 5%)

Question 4

For a continuously payable annuity at a constant force of interest δ, the present value of payments made continuously at rate 1 per year for T years is:

Accepted Answer

ā(T) = (1 - e^(-δT)) / δ

Answer

ā(T) = (e^(δT) - 1) / δ

Answer

ā(T) = T × e^(-δ)

Answer

ā(T) = 1 - e^(-Tδ)

Question 5

An investor wants to accumulate $100,000 in 15 years by making level annual deposits at the end of each year into an account earning 6% annually. How much should each annual deposit be?

Accepted Answer

$4,296.28

Answer

$5,000.00

Answer

$3,974.08

Answer

$6,666.67

Question 6

Which of the following statements about perpetuities is CORRECT?

Accepted Answer

The future value of a perpetuity evaluated at time n grows without bound as n → ∞

Answer

A perpetuity-due has a lower present value than a perpetuity-immediate with the same payments

Answer

A perpetuity-immediate paying $C per year at rate i has present value C/d

Answer

A perpetuity paying $C annually at rate i has present value C × i

Question 7

The yield rate (internal rate of return) of an investment is defined as the interest rate i at which:

Accepted Answer

The present value of all cash outflows equals the present value of all cash inflows

Answer

The net present value of the investment is maximized

Answer

The future value of all payments equals the original investment amount

Answer

The investment generates the highest possible nominal return