Question

Finding the discounted value of $1,000 to be received at the end of each of the next five years requires calculating the:

Select one:

a. future value of an annuity.

b. future value of a deferred annuity.

c. present value of an annuity.

d. present value of a deferred annuity.

A cash flow projected today for a future period of time is a:

Select one:

a. present value of a single sum.

b. future value of a single sum.

c. present value of an annuity.

d. future value of an annuity.

​Peter recently purchased a new home with a 25-year mortgage loan of $250,000 at 8% compounded monthly, What is the total amount Peter will pay the bank over the life of the loan?

Select one:

a. ​$23,420

b. ​$328,860

c. ​$250,000

d. ​$578,860

Answer 1

a)

a. future value of an annuity

Annuity is a series of fixed payment for a fixed time. Annuities are made at the end of the period.

b)

a. present value of a single sum

A cash flow that is paid in the future projected today is called the present value of that future cash flow.

c)

Rate = 8% / 12 = 0.6667%

Number of periods = 25 * 12 = 300

Present value = Annuity * [1 - 1 / (1 + r)ⁿ] / r

250,000 = Annuity * [1 - 1 / (1 + 0.006667)³⁰⁰] / 0.006667

250,000 = Annuity * 129.560075

Annuity = 1,929.6068

Total amount = 1,929.6068 * 300

Total amount = 578,860