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Suppose a recent college graduate's first job allows her to deposit $150 at the end of each month in a savings plan that earns 6%, compounded monthly. This savings plan continues for 9 years before new obligations make it impossible to continue. If the accrued amount remains in the plan for the next 15 years without deposits or withdrawals, how much money will be in the account 24 years after the plan began

Respuesta :

facundobuzzetti

Answer:

Final Value= $51,312.68

Explanation:

Giving the following information:

Monthly deposit= $150

Interest rate= 0.06/12= 0.005

Number of months= 9*12= 108

First, we need to calculate the future value of the first investment. We will use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= monthly deposit

FV= {150*[(1.005^108)-1]} / 0.005

FV= $21,410.99

The second part of the investment:

Number of years= 15

Annual interest rate= 6%

I will assume that the interest rate is annually compounded now. If this is not the case, just change the interest rate (0.005) and "n" (15*12=180)

We need to use the following formula:

FV= PV*(1+i)^n

FV=21,410.99* (1.06^15)

FV= $51,312.68

The money that should be in the account 24 years after the plan began is a Final Value $51,312.68.

Calculation of the amount after 24 years when the plan started:

Since

  • Monthly deposit= $150
  • Interest rate= 0.06/12= 0.005
  • Number of months= 9*12= 108

Now first determine the future value

So,

FV= {A*[(1+i)^n-1]}/i

here.

A= monthly deposit

So,

FV= {150*[(1.005^108)-1]} / 0.005

FV= $21,410.99

Now

Number of years= 15

Annual interest rate= 6%

We know that

FV= PV*(1+i)^n

FV=21,410.99* (1.06^15)

FV= $51,312.68

Hence, The money that should be in the account 24 years after the plan began is a Final Value $51,312.68.

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