Question

Starting at the end of this year, you plan to make annual deposits of $5,000 for the next 10 years followed by deposits of $13,000 for the following 10 years. The deposits earn interest of 4.6%. What will the account balance be by the end of 33 years? Round to the nearest cent

You are interested in buying a house and renting it out. You expect to receive a monthly net income of $1450 from rent. You then expect to sell the house for $329,000 at the end of 54 months. If your discount rate on this investment is 9% per year (compounded monthly), how much is this property worth to you today? Assume that you receive rent at the beginning of each month and you receive the first rent the same day you purchase the property. Round to the nearest cent

Answer 1

Solution

a. Here the Account balanc at end of 33 years will be = Future value 5000 deposited for 10 years at end of 33 years+Future value 13000 deposited for 10 years, at end of 33 years

Now future value of annuity=Annuity amount*(((1+r)^n-1)/r)

where

r-intrest rate per period

n-number of periods

Now for the 5000 deposited for 10 years

Future value of annuity=5000*(((1+.046)^10-1)/.046)=61727.67

Now this amount(61727.67)will agin be deposited for 23 more years

Future value of a cashflow=Cashflow*(1+i)^m

where

iintrest rate

m-number of periods

Future value of 61727.67 =61727.67*(1+.046)^23

=$173663.53 (Future value of 5000 deposited for 10 years ,at the end of 33 years)

Similarly for 13000 deposited for 10 years

Future value of annuity=13000*(((1+.046)^10-1)/.046)=160491.93

Now this amount(160491.93)will agin be deposited for 13 more years

Future value of 160491.93 =160491.93*(1+.046)^13

=287981.84 (Future value of 13000 deposited for 10 years ,at the end of 33 years)

Thus total account balance at end of 33 years=173663.53+287981.84

Thus total account balance at end of 33 years=$461645.37

b. The worth of the property today=Present value of annuity payments of rent+Present value of selling price of house

Present value of annuity due=Annuity payment*((1-(1/(1+r)^n))/r)*(1+r)

Present value of a cashflow=Cashflow/(1+r)^n

where

r-intrest rate per period-9/12=.75%per month

n-number of periods -54

Annuity payment=monthly rent=1450

Cashflow-Selling price of property=329000

Putting values

The worth of the property today=(1450*((1-(1/(1+.0075))^54))/.0075)*(1+.0075)+329000/(1+.0075)^54

The worth of the property today=$284438.12

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