Question

What is the value today of a money machine that will pay $2,450.00 per year for 11.00 years? Assume the first payment is made one year from today and the interest rate is 8.00%.

Answer format: Currency: Round to: 2 decimal places.

Answer 1

The given scenario is a case of Ordinary Annuity where we receive fixed amount of annuity at the end of every period.

Present value of an ordinary annuity = A * [ 1 - (1+r)^-n ] / r

where, A is the Annuity amount per period, r is the interest/discount rate per period, n is the number of periods

In our case A = $2,450

n = 11 years

r = 8.00% per year

Present value of the given annuity = 2450 * [ 1 - ((1+0.08)^-11) ] / 0.08

=> 2450 * [ 1 - (1.08^-11) / 0.08

=> 2450 * [ 1 - 0.4288829 ] / 0.08

=> 2450 * 0.5711171 / 0.08

=> 17,490.4611875

=> $17,490.46 (rounded off)