Question

Annuity A requires annual contributions over 5 years and pays 5% annual interest. Annuities B and C have the same interest rate and annual contributions, but have a term of 10 and 30 years respectively. Each annuity has $50, 000 in it at the end of its term. Which of the following answers correctly lists all of the annuities that have a greater amount of interest in them than the sum of contributions over their term? Select the correct answer below:
A. Annuity C
B. Annuity A
C. Annuity B
D. Annuity B and C

Answer 1

Answer:

A. Annuity C

Explanation:

we can use the present value of an ordinary annuity formula to determine the annual contributions:

FV annuity factor, 5%, 5 periods = 5.5256

FV annuity factor, 5%, 10 periods = 12.578

FV annuity factor, 5%, 30 periods = 66.439

annual contribution annuity A = $50,000 / 5.5256 = $9,048.79, total annuity payments = $45,243.95, so accumulated interests are $4,756.05

annual contribution annuity B = $50,000 / 12.578 = $3,975.19, total annuity payments = $39,751.90, so accumulated interests are $10,248.10

annual contribution annuity C = $50,000 / 66.439 = $752.57, total annuity payments = $22,577.10, so accumulated interests are $27,422.90