Deryl wishes to save money to provide for his retirement. Beginning one year fro

Question

Deryl wishes to save money to provide for his retirement. Beginning one year from now. he will begin depositing the same fixed amount each year for the next 30 years into a retirement savings account. Starting one year after making his final deposit, he will withdraw $100,000 annually for each of the following 25 years (i.e. he will make 25 withdrawals in all). Assume that the retirement fund earns 12% annually over both the period that he is depositing money and the period he makes withdrawals. In order for Deryl to have sufficient funds in his account to fund his retirement, how much should he deposit annually (rounded to the nearest dollar)? $97.368 $2.902 $3.250 $2.730 $3.640 You have just received an advertisement from Corleone Inc.. a "paycheck loan" service. Corleone will charge you a fee of 5% for a two-week loan (i.e. if you borrow $100, you must repay $105 in two week's time). Assuming a 52 week year, what is the Effective Annual Rate (EAR) that Corleone charges (rounded to the nearest whole percent)? 130% 356% 5% 256% 230%

Explanation / Answer

8)

Present value of annuity = P×[1-(1÷(1+r)^n)]÷r

r is interest rate per period

P is payment per period

n is number of payments

= $100,000×[1-(1÷(1+25%)^25)]÷12%

Retirement fund required = $830,185.09

Future value of annuity = P×[(1+r)^n-1]÷r

r is interest rate per period

P is payment per period

n is number of payments

$830,185.09 = P×[(1+12%)^30-1]÷12%

Annual deposit required, P = $3,440

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