Question

Assume you are to receive a 10-year annuity with annual payments of $800. The first payment will be received at the end of year 1, and the last payment will be received at the end of year 10. You will invest each payment in an account that pays 7 percent compounded annually. Although the annuity payments stop at the end of year 10, you will not with draw any money from the account until 20 years from today, and the account will continue to earn 7 percent for the entire 20-year period. What will be the value in your account at the end of year 20 (round to the nearest dollar)

Answer 1

The question is solved by first computing the future value of the first 10-year payments.

Information provided:

Annual payment= $800

Time= 10 years

Interest rate= 7%

The future value is calculated by entering the below in a financial calculator:

PMT= 800

N= 10

I/Y= 7

Press CPT and FV to compute the future value.

The value obtained is 11,053.16.

Therefore, the future value of the annuity is $11,053.16.

Next, the future value of the first 10-year payments.

Information provided:

Present value = $11,053.16

Time= 10 years

Interest rate= 7%

The future value is calculated by entering the below in a financial calculator:

PV= -11,053.16

N= 10

I/Y= 7

Press CPT and FV to compute the future value.

The value obtained is 21,743.24.

Therefore, the value in my account at the end of 20 years is $21,743.24.

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