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question 13
You want to have $12,500 in 12 years. You will invest how much into an account that has an annual rate of 5.5% compounded daily?

Round your answer to two decimal places. Do not include the $ sign in your answer.

Assume 365 days per year.
question 14
You wish to deposit $200 each month over the next 13 years into an account that has an annual rate of 5.3% compounded monthly. How much is in the account at the end of 13 years?
Round your answer to two decimal places.
question 15
You want to save up $14,000 to purchase a used car in 2 years. Your account earns an annual rate of 6.7% compounded monthly. How much do you need to deposit each month to meet your goal?

Respuesta :

The amount to be invested today so as to have $12,500 in 12 years is  $6,480.37.

The amount that would be in my account in 13 years is $44,707.37.

The amount I need to deposit now is $546.64.

How much should be invested today?

The amount to be invested today = future value / (1 + r)^nm

Where:

  • r = interest rate = 5.5 / 365 = 0.015%
  • m = number of compounding = 365
  • n = number of years  = 12

12500 / (1.00015)^(12 x 365) = $6,480.37

What is the future value of the account at the end of 13 years?

Future value = monthly deposits x annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

  • r = interest rate = 5.3 / 12 = 0.44%
  • n = 13 x 12 = 156

200 x [{(1.0044^156) - 1} / 0.0044] = $44,707.37

What should be the monthly deposit?

Monthly deposit = future value / annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

  • r = 6.7 / 12 = 0.56%
  • n = 2 x 12 = 24

$14,000 / [{(1.0056^24) - 1} / 0.0056] = $546.64

To learn more about annuities, please check: https://brainly.com/question/24108530

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