Jack inherited a perpetuity-due, with annual payments of 15,000. He immediately exchanged the perpetuity for a 25-year annuity-due having the same present value. The annuity-due has annual payments of X. All the present values are based on an annual effective interest rate of 10% for the first 10 years and 8% thereafter. Calculate X.

X=17,384.37

Step-by-step explanation:

The present value of the perpetuity can be calculated by discounted for the different interest rates:

#Now, we use the annuity-due present value factor to get the present values of the annuity payments, let X be the annual annuity payments;

Hence, the value of X is 17,384.37

alot

step-by-step explanation:

its a wood chuck that can chuck wood

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560