Question

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1. You have saved $5,000 for a down payment on a new car. The largest monthly payment you can afford is $400. The loan will have an 11% APR based on end-of-month payments.

What is the most expensive car you can afford if you finance it for 48 months? Do not round intermediate calculations. Round your answer to the nearest cent.
$  

What is the most expensive car you can afford if you finance it for 60 months? Do not round intermediate calculations. Round your answer to the nearest cent.

2. Find the present values of these ordinary annuities. Discounting occurs once a year. Do not round intermediate calculations. Round your answers to the nearest cent.

1. $400 per year for 14 years at 8%.

   $  

2. $200 per year for 7 years at 4%.

   $  

3. $700 per year for 8 years at 0%.

   $  

4. Rework previous parts assuming they are annuities due.

   Present value of $400 per year for 14 years at 8%: $  

   Present value of $200 per year for 7 years at 4%: $  

   Present value of $700 per year for 8 years at 0%: $  

Answer 1

Answer 1-a

Answer 2-a

Calculation of total cost of new car

We can use the present value of annuity formula to calculate the present value.

Total cost of new car = Down payment + Finance amount

Present value of annuity = P x {[1 - (1+r)^-n]/r}

Down payment = $5000

Present Value of annuity = ?

P = annuity = $400

Calculation of finance amount

r = interest rate = 8%

We can use the present value of annuity formula to calculate the Finance amount

n = number of years = 14

Present value of annuity = P x {[1 - (1+r)^-n]/r}

Present value of annuity = 400 x {[1 - (1+0.08)^-14]/0.08}

Present Value of annuity = finance amount = ?

Present value of annuity = 400 x 8.244237

P = Loan monthly payment = $400

Present value of annuity = 3297.69

r = interest rate per month = 11%/12 = 0.009167

Present Value of ordinary annuity = $3,297.69

n = number of months loan payment = 48

Present value of annuity = 400 x {[1 - (1+0.009167)^-48]/0.009167}

Answer 2-b

Present value of annuity = 400 x 38.69142

We can use the present value of annuity formula to calculate the present value.

Present value of annuity = 15476.57

Present value of annuity = P x {[1 - (1+r)^-n]/r}

Finance amount = $15,476.57

Present Value of annuity = ?

P = annuity = $200

Total cost of new car = $5000 + $15,476.57

r = interest rate = 4%

Total cost of new car = $20,476.57

n = number of years = 7

You can afford car costing $20,476.57 if you finance it for 48 months.

Present value of annuity = 200 x {[1 - (1+0.04)^-7]/0.04}

Present value of annuity = 200 x 6.002055

Answer 1-b

Present value of annuity = 1200.41

Calculation of total cost of new car

Present Value of ordinary annuity = $1,200.41

Total cost of new car = Down payment + Finance amount

Down payment = $5000

Answer 2-c

We can use the present value of annuity formula to calculate the present value.

Calculation of finance amount

Present value of annuity = P x {[1 - (1+r)^-n]/r}

We can use the present value of annuity formula to calculate the Finance amount

Present Value of annuity = ?

Present value of annuity = P x {[1 - (1+r)^-n]/r}

P = annuity = $700

Present Value of annuity = finance amount = ?

r = interest rate = 0%

P = Loan monthly payment = $400

n = number of years = 8

r = interest rate per month = 11%/12 = 0.009167

Present value of annuity = 700 x {[1 - (1+0.00)^-8]/0.00}

n = number of months loan payment = 60

Present value of annuity = 700 x 0

Present value of annuity = 400 x {[1 - (1+0.009167)^-60]/0.009167}

Present value of annuity = 700

Present value of annuity = 400 x 45.99303

Present Value of ordinary annuity = $700

Present value of annuity = 18,397.21

Finance amount = $18,397.21

Total cost of new car = $5000 + $18,397.21

Total cost of new car = $23,397.21

You can afford car costing $23,397.21 if you finance it for 60 months.