The time value of moneyConsider the following scenarios:Simon FamilyThe Simons have saved $5,000 towards their goal to have $45,000 for a down payment on a house in 6 years. They will put the $5,000 in an account along with money they will deposit annually. They donât know how much that annual deposit should be, so theyâve asked you to calculate it. They have found a savings institution that will pay 6% interest.Perkette FamilyThe Perkettes have set a goal to have $45,000 for a down payment on a house in 6 years. They have not saved anything so far. They have asked you to calculate how much they will need to put away each year to achieve their $45,000 down-payment goal. They have found a savings institution that will pay 6% interest.Use the scenarios along with the following factor table data. Note that the complete Future Value and Future Value Annuity tables (as well as the Present Value and Present Value Annuity tables) are located in the appendix in your text.Table of Future Value Factors:Interest RateYear 5% 6% 8%1 1.050 1.060 1.0802 1.102 1.120 1.1663 1.158 1.190 1.2604 1.216 1.260 1.3605 1.276 1.340 1.4696 1.340 1.420 1.5878 1.477 1.590 1.85110 1.629 1.790 2.159Table of Future Value Annuity Factors:Interest RateYear 5% 6% 8%1 1.000 1.000 1.0002 2.050 2.060 2.0803 3.152 3.180 3.2464 4.310 4.380 4.5065 5.526 5.630 5.8676 6.802 6.970 7.3368 9.549 9.890 10.63710 12.578 13.180 14.4871. What is the amount of money the Simons will need to deposit annually (rounded to the nearest two decimal places) to achieve their down-payment goal?2. What is the amount of money the Perkettes will need to deposit annually (rounded to the nearest two decimal places) to achieve their down-payment goal?

Respuesta :

Answer:

annual payment = $5,496.25

Explanation:

the $5,000 that they deposit today will be worth $5,000 x (1 + 6%)⁶ = $6,691.13 in 6 years.

this means that they need to save an extra $45,000 - $6,691.13 = $38,308.87

we can calculate the amount that they need to deposit at the end of every year to have $38,308.87 in 6 years by using the future value of an annuity formula:

FV = payment x annuity factor

payment = FV / annuity factor

  • FV = $38,308.87
  • FV annuity factor, 6%, 6 periods = 6.970

annual payment = $38,308.87 / 6.97 = $5,496.25