2. Suppose you borrow $2,000 at 5% and you are going to make annual payments of $734.42. How long before you pay off the loan
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Answer:
Ans. Assuming that the withdrawal period is 300 months (25 years), you can withdraw every month $15,547.96
Explanation:
Hi, first, we have to take to future value (30 years in the future) the invested capital (both the stock account and the bond account). From there, we will consider the sum of both future values as the present value of the annuity that you are about to receive for the next 25 years (300 months). But before we do all that, we need to convert the return rates (compounded monthly) into effective monthly rates, for that we just go ahead and divide each one by 12, as follows
r(Stock) = 0.105/12= 0.00875
r(Bond)= 0.061/12 = 0.00508
r(Combined Account)= 0.069/12=0.00575
Now we are ready, first, let´s find the future value of the stock account.
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Now, let´s find out how much will it be in 30 years, investing $325 per month, at the end of the month, at 0.508% effective monthly.
And then we add them up and we get:
Ok, now let´s find the annuity (monthly withdraw) taking into account that we are going to make 300 withdraws at a rate of 0.575% effective monthly,
\frac{A((1+0.00575)^{300}-1) }{0.00575(1+0.00575)^{300} }[/tex]
Best of luck.