Assume you are to receive a 20-year annuity with annual payments of $50. The first payment will be received at the end of Year 1, and the last payment will be received at the end of Year 20. You will invest each payment in an account that pays 10 percent. What will be the value in your account at the end of Year 30?

The answer is $7,427.71

Explanation:

The formula for future value annuity factor A [{ (1+r) ^n - 1}:r

where A is the annuity amount

n is the number of time periods

r is the interest rate.

A is $50

n is 20 years

r is 10% or 0.1

$50 [{ (1+0.1) ^20 - 1} : 0.1

$50 [{ (1.1^20) - 1} : 0.1]

$50 [{6.7275 - 1} : 0.1]

$50 [5.7275 : 0.1]

$50 x 57.275

=$2.863.75

The formula to use for the next 30 years is: PV (1+r) ^n

Now future value for year 30:

The new year (n) will be 30 years - 20 years = 10 years

rate is still 10%

Present Value (PV) is $2.863.75

$2,863.75 (1+0.1) ^10

$2.863.75 (1.1) ^10

$2.863.75 x 2.5937

= $7,427.71