Question

Suppose you just bought a 25-year annuity of $8,200 per year at the current interest rate of 12 percent per year. What is the value of your annuity today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value $ What is the present value if interest rates suddenly drop to 7 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value $ What is the present value if interest rates suddenly rise to 17 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value $

Answer 1

Answer:

64,313.74 ; 95,559.38 ; 47,283.11

Explanation:

by definition the present value of an annuity is given by:

$a_{n} =P*\frac{1-(1+i)^{-n} }{i}$

where $a_{n}$ is the present value of the annuity, $i$ is the interest rate for every period payment, n is the number of payments, and P is the regular amount paid. so applying to this particular problem, we have:

1. P=8,200, n=25, i=12%

$a_{n} =8,200*\frac{1-(1+12\%)^{-25}}{12\%}$

$a_{n} =64,313.74$

2. P=8,200, n=25, i=7%

$a_{n} =8,200*\frac{1-(1+7\%)^{-25} }{7\%}$

$a_{n} =95,559.38$

3. P=8,200, n=25, i=17%

$a_{n} =8,200*\frac{1-(1+17\%)^{-25} }{17\%}$

$a_{n} =47,283.11$