Question

Which of the following statements about annuities are true? Check all that apply. An annuity due is an annuity that makes a payment at the beginning of each period for a certain time period. An annuity due earns more interest than an ordinary annuity of equal time. Ordinary annuities make fixed payments at the beginning of each period for a certain time period. An annuity is a series of equal payments made at fixed intervals for a specified number of periods. Which of the following is an example of an annuity? A job contract that pays an hourly wage based on the work done on a particular day A job contract that pays a regular monthly salary for three years Katie had a high monthly food bill before she decided to cook at home every day in order to reduce her expenses. She starts to save $1,130 every year and plans to renovate her kitchen. She deposits the money in her savings account at the end of each year and earns 12% annual interest. Katie's savings are an example of an annuity. If Katie decides to renovate her kitchen, how much would she have in her savings account at the end of six years? $9,170.16 $10,270.58 $4,645.89 $7,794.64 If Katie deposits the money at the beginning of every year and everything else remains the same, she will save by the end of six years.

Answer 1

Part 1:

Correct statement are: 1, 2 and 4

Annuities are set of equal cash flow payments that are made for a particular time period periodically. Annuities due are those where periodic cash flows are made at the beginning of the period (compared to ordinary annuities, where the periodic cash flows are made at the end of the period). Also, given the amount in annuity due, since made at beginning of the period, would compound for an extra period and hence would earn higher interest compared to an ordinary annuity.

Part 2:

Option 2. Since regular payments are made for 3 years (on monthly basis). In option 1, wages are paid based on hours but only once.

Part 3:

This is an ordinary annuity.

FV of Annuity =P (1 + r)" - 1 14 P= Periodic Payment r = rate per period number of periods n =

$FV = 1,130 * [\frac{(1+0.12)^{6} - 1}{0.12}]$

FV = $1,130 * 8.1152

FV = $9,170.64 (Closest to Option 1)

Part 4:

This would now be an annuity due.

FV of Annuity Due = (1 + r) x P [(1 + r)" - 11 1 P= Periodic Payment r=rate per period n = number of periods

$FV = 1,130 * [\frac{(1+0.12)^{6} - 1}{0.12}] * (1 + 0.12)$

FV = $1,130 * 8.1152 * 1.12

FV = $10,270.58