Question

The Pirerras are planning to go to Europe 3 years from now and have agreed to set aside $140/month for their trip. If they deposit this money at the end of each month into a savings account paying interest at the rate of 9.5%/year compounded monthly, how much money will be in their travel fund at the end of the third year? (Round your answer to the nearest cent.)
The Johnsons have accumulated a nest egg of $16,000 that they intend to use as a down payment toward the purchase of a new house. Because their present gross income has placed them in a relatively high tax bracket, they have decided to invest a minimum of $1000/month in monthly payments (to take advantage of the tax deduction) toward the purchase of their house. However, because of other financial obligations, their monthly payments should not exceed $1300. If the Johnsons decide to secure a 15-year mortgage instead of a 30-year mortgage, what is the price range of houses they should consider when the local mortgage rate for this type of loan is 8%/year compounded monthly? (Round your answers to the nearest cent.)
least expensive $ 1
most expensive $ 2

Answer 1

Answer:

(a)$5805.21

(b)Least Expensive Mortgage =$120640.59

Most Expensive Mortgage =$152032.77

Step-by-step explanation:

The future value of an ordinary annuity with deposits P made regularly k times each year for n years, with interest compounded times k per year at an annual rate r, is given as:

$F.V.=\dfrac{P[(1+i)^{kn}-1]}{i}$

The Pirerra's Monthly Payments=$140

Annual Rate =9.5%

Therefore: Monthly Rate=0.095/12

Years, n=3

Period, k=12

$F.V.=\dfrac{140[(1+\frac{0.095}{12} )^{3*12}-1]}{\frac{0.095}{12} }=\ 5805.21$

(b)For the Johnsons, Present value of Mortgage is derived using the formula:

$\Text{Present Lump Sum}, A_0=\dfrac{P[1-(1+i)^{-kt}]}{\frac{r}{k} }$

At $1000 Monthly payment

$\Text{Present Lump Sum}, A_0=\dfrac{1000[1-(1+\frac{0.08}{12} )^{-12*15}]}{\frac{0.08}{12} }=\ 104640.59$

Adding  a down payment of $16000

• Least Expensive Mortgage = 104640.59+16000=$120640.59

At $1300 Monthly Payment

$\Text{Present Lump Sum}, A_0=\dfrac{1300[1-(1+\frac{0.08}{12} )^{-12*15}]}{\frac{0.08}{12} }=\ 136032.77$

Adding  a down payment of $16000

• Most Expensive Mortgage = 136032.77+16000=$152032.77