Question

1. You have $2,500 on a credit card that charges a 12% interest rate. If you want to pay off the credit card in 3 years, how much will you need to pay each month (assuming you don't charge anything new to the card)?

2.   You want to buy a $228,000 home. You plan to pay 10% as a down payment, and take out a 30 year loan for the rest.

a) How much is the loan amount going to be?
b) What will your monthly payments be if the interest rate is 6%?

c) What will your monthly payments be if the interest rate is 7%?

3. You can afford a $1400 per month mortgage payment. You've found a 30 year loan at 8% interest.
a) How big of a loan can you afford?

b) How much total money will you pay the loan company?

c) How much of that money is interest?

4. ind the time required for an investment of 5000 dollars to grow to 6200 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Round your answer to two decimal places
Your answer is t= ____years

Answer 1

Answer to Question 1:

Amount Outstanding = $2,500
Time Period = 3 years or 36 months

Annual Interest Rate = 12.00%
Monthly Interest Rate = 1.00%

Let monthly payment be $x

$2,500 = $x/1.01 + $x/1.01^2 + … + $x/1.01^35 + $x/1.01^36
$2,500 = $x * (1 - (1/1.01)^36) / 0.01
$2,500 = $x * 30.107505
$x = $83.04

Monthly Payment = $83.04

Answer to Question 2:

Part a:

Cost of Home = $228,000

Down Payment = 10% * Cost of Home
Down Payment = 10% * $228,000
Down Payment = $22,800

Amount Borrowed = Cost of Home - Down Payment
Amount Borrowed = $228,000 - $22,800
Amount Borrowed = $205,200

Part b:

Amount Borrowed = $205,200
Time Period = 30 years or 360 months

Annual Interest Rate = 6.00%
Monthly Interest Rate = 0.50%

Let monthly payment be $x

$205,200 = $x/1.005 + $x/1.005^2 + … + $x/1.005^359 + $x/1.005^360
$205,200 = $x * (1 - (1/1.005)^360) / 0.005
$205,200 = $x * 166.791614
$x = $1,230.28

Monthly Payment = $1,230.28

Part c:

Amount Borrowed = $205,200
Time Period = 30 years or 360 months

Annual Interest Rate = 7.00%
Monthly Interest Rate = 0.5833%

Let monthly payment be $x

$205,200 = $x/1.005833 + $x/1.005833^2 + … + $x/1.005833^359 + $x/1.005833^360
$205,200 = $x * (1 - (1/1.005833)^360) / 0.005833
$205,200 = $x * 150.313637
$x = $1,365.15

Monthly Payment = $1,365.15