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In: Finance

You’d like to buy a small ranch when you retire in 40 years. You estimate that...

You’d like to buy a small ranch when you retire in 40 years. You estimate that in 40 years you’ll need $7 million to do so. If your savings can earn 1.1% per month, how much will you need to save each month (for 40 years), starting next month, in order to reach your goal? Round to the nearest cent. ​[Hint: Note that the question gives us the monthly interest rate. This is the periodic rate, which is i/m in our formulas. Don't divide it by m again when plugging in the formula.]

Starting at the end of this year, you plan to make annual deposits of $8,000 for the next 10 years followed by deposits of $9,000 for the following 10 years. The deposits earn interest of 7.0%. What will the account balance be by the end of 25 years? Round to the nearest cent. ​[Hint: There are two annuities. Convert them to single cash flows using the FV annuity formula, then move the values to the end of year 25.]

Following her 18th birthday, Madison began investing $50 at the end of each week in an account earning 4% per year. She plans to continue making weekly investments until she turns 68. If she hadn't started investing until she turned 60, how much would she have to invest each week in order to have the same retirement nest egg at age 68? Round to the nearest cent. ​[Hint: Find the size of the retirement nest egg under the first long horizon scenario, then use that number to solve for CF under the short investment horizon scenario.]

Solutions

Expert Solution

First question:

Amount to be saved every month= $405.71 as follows:

Second question:

FV of first annuity= $8,000(FVA 7%,10) = 8000* 13.816448 = $110,531.58

FV of this amount at the end of further 15 years (total 25 years)= $110,531.58*FVIF(7%,15)

=110,531.58 * 2.75903154 = $ 304,960.13

FV of second annuity= $9,000(FVA 7%,10=9000* 13.816448 = $124,348.03

FV of this amount at the end of further 5 years = $ 124348.03*FVIF(7%,5)

= 124,348.03* 1.402552 = $ 174,404.55

Total value at the end of 5 years= 304960.13 + 174404.55 = $479,364.68

Third question:

Commencing at the age of 60, weekly investment needed= $846.70

Calculation as below:

jeff jeffy answered 1 year ago
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