Question

4. You have just paid your subscription to Investing Wisely Weekly through the end of this year. You plan to subscribe to the magazine for the rest of your life. You have two options.

You can either renew the subscription annually by paying $85 at the end of each year or you can get a lifetime subscription for $620 payable immediately.

Assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant, how many years (include at least 2 decimals if necessary) must you live to make the lifetime subscription the better buy?

5. You agree to make 24 deposits of $500 at the end of each month into a bank account. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominalannual interest rate will you be earning?

6. You turn 35 today, and you plan to save $2,000 each month for retirement, with the first deposit made at the end of this month. You plan to retire 30 years from today, when you turn 65, and expect to live for 25 years after retirement, until age 90. Under these assumptions, how much can you spend each month after you retire? Your first withdrawal will be made at the end of the first month of retirement.

You will invest in a mutual fund that's expected to provide a return of 4.5% per year, compounded monthly throughout your life.

7. Keenan Industries has a bond outstanding with an 8.25% coupon, payable semiannually, and a $1,000 par value. The bond's dollar price is $1,066.00 The bond has a 7.47% yield to call, but it can be called in 6 years. What is the bond’s call price?

Answer 1

Solution 4:

Given:

Annual Subscription = $85

Lifetime Subscription = $620

Return on Investment = 6%

Therefore,

Number of years for which Purchase of Lifetime Subscription will be justified =

620 = 85 * [{(1+0.06)years-1}/0.06]      {Formula of Future Value of Annuity = Annuity * [{1+rate)no. of years-1}/rate]

620 = (85*1.06years-1)/0.06

620 = 1416.666667(1.06years-1)

620/1416.666667 = 1.06years-1

0.437647 = 1.06years-1

0.437647+1 = 1.06years

1.437647 = 1.06years

Using Log:

Log1.06 1.437647 = years

Using change of base rule of log :

Log 1.437647/Log 1.06 = years

it implies,

years = 0.157652/0.025306

years = 6.23 years

Or by using Excel Function NPER :

=NPER(0.06,85,620) NPER(rate, pmt, py, [fv], [type])

=NPER(0.06,85,620) NPER(rate, pmt, py, [fv], [type])

Conclusion : Lifetime subscription will only be beneficial if we are going to take benefit from for more than 6.23 years that is for at least 7 years.