An annuity-immediate with 20 annual payments starts with a payment of 300 and each payment thereafter...

An annuity-immediate with 20 annual payments starts with a payment of 300 and each payment thereafter is 25 more than the previous payment. The effective annual interest rate is 5%.
Calculate the present value. Be sure to include the appropriate equation or expression of value that you use. Instead of a 20 year annuity-immediate, it is a perpetuity. What would the present value be in that case?

Expert Solution

The formula used for a growing annuity is:

where, PMT is the payment per period, in this case, 300

r and g are the interest rate and growth rate respectively

n is the number of years/periods

g=2.5% (assuming a printing error as otherwise the calculation is mathematically not possible)

r=5%

PV=(300/(0.05-0.025)*[1-(1.025/1.05)²⁰]= 4589.0723

Now, if it were a perpetuity, PV=PMT/(r-g)

So, PV=300/0.025= 12000

jeff jeffy answered 2 years ago

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