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Suppose you want to accumulate $120,000 for your retirement in 30 years.
Consider these two plans:

Plan A: make a single deposit into an account with an annual compounding and an APR of 5%.
Plan B: Make a single deposit into an account with continuous compounding and an APR of 4.8% 

1.) how much do you need to deposit in each amount in order to reach the goal?
2.) calculate the current APR the compounding period, and the claimed APY for your personal savings account. (Or pick a rate from a nearby bank)
3.) calculate the APY on your account (or someone u know)
4.) Does your calculation agree with the APY claimed by the bank?

Respuesta :

jayilych4real

The amount that would be needed to be deposited in order to reach the goal is:

  • Plan A: $27,765.29.
  • Plan B: $28,431.33

Calculations and Parameters:

Since Plan A compounds annually at an apr of 5%.

and plan B compounds continuously at an apr of 4.8%

PART A

Using the formula for annual compounding

[tex]f = p * (1+r)^n[/tex]

Where

  • f is the future value which is equal to 120,000
  • p is the present value.
  • r is the interest rate per time period.
  • n is the number of time periods.

Because the compounding is done annually, then the APR/100= 0.05

Also, because the time periods are annual, hence, the time periods would be equal to the number of years = 30.

Putting the values together:

120,000 = p * (1.05)^30.

divide both sides of this formula [tex](1.05)^3^0[/tex] to get:

[tex]120,000 / (1.05)^3^0[/tex] = p which makes p equal to $27,765.29.

PART B

To solve for the PART B answer

the formula for continuous compounding is:

[tex]f = p * e^(r*n)[/tex]

Where

  • r is the interest rate per time period which is in years.
  • n is the number of time periods which is in years.

The formula becomes:

[tex]120,000 = p * e^(.048 * 30).[/tex]

divide both sides of this equation by [tex]3^(.048 * 30)[/tex] to get:

[tex]120,000 / (e^(.048*30))[/tex] = p which makes p equal to $28,431.33.

#SPJ1

Read more about compound interest here:

https://brainly.com/question/24274034