A man buys a car for 37000 If the interest rate on the loan

A man buys a car for $37,000. If the interest rate on the loan is 12%, compounded monthly, and if he wants to make monthly payments of $700 for 48 months, how much must he put down? (Round your answer to the nearest cent.) $ A couple purchasing a home budget $1400 per month for their loan payment. If they have $27,000 available for a down payment and are considering a 25-year loan, how much can they spend on the home at each of the following rates? (Round your answers to the nearest cent.) 6.3% compounded monthly $ 7.1% compounded monthly $ A couple who borrow $100,000 for 15 years at 8.4%, compounded monthly, must make monthly payments of $978.89. Find their unpaid balance after 1 year. (Round your answer to the nearest cent.) $ During that first year, how much interest do they pay? (Round your answer to the nearest cent.) $

Solution

(1)

In this problem, first we calculate the present value of the cash flow stream of $700 per month for the period of 48 months.

P = PMT x ((1 - (1 / (1 + r) ^ n)) / r)

Where:

P = the present value of an annuity stream (to be found)

PMT = the dollar amount of each annuity payment ($700)

r = the interest rate (also known as the discount rate) (1% per month)

n = the number of periods in which payments will be made (48 months)

P = 700 * ((1 - (1 / (1 + 1%) ^ 48)) / 1%) = $26,581.77

Total Loan Amount = $37,000

Down Payment = $37,000 -  $26,581.77 = $10,418.23

(2)

(a) In this problem, first we calculate the present value of the cash flow stream of $1400 per month for the period of 48 months.

P = PMT x ((1 - (1 / (1 + r) ^ n)) / r)

Where:

P = the present value of an annuity stream (to be found)

PMT = the dollar amount of each annuity payment ($1400)

r = the interest rate (also known as the discount rate) (6.3%/12 = 0.525% per month)

n = the number of periods in which payments will be made (25 * 12 = 300 months)

P = 1400 * ((1 - (1 / (1 + 0.525%) ^ 300)) / 0.525%) = $2,11,236.75

They have $27,000 available for down payment, hence total loan budget will be

$2,11,236.75 +  $27,000 = $2,38,236.75

(b) with interest rate 7.1%

P = $1,96,306.29

Budget =  $1,96,306.29 + $27000 = $2,23,306.29

(3)

(a) As per formula mentioned above calculate the Present Value (P) for 1 year

P = the present value of an annuity stream (to be found)

PMT = the dollar amount of each annuity payment ($978.89)

r = the interest rate (also known as the discount rate) (8.4%/12 = 0.700% per month)

n = the number of periods in which payments will be made (1 * 12 = 12 months)

P = 978.89 * ((1 - (1 / (1 + 0.700%) ^ 12)) / 0.700%) = $11,229.22

At the end of 1 year, $11,229.22 is paid off.

Unpaid balance after 1 year = $100000 - $11,229.22 = $88,770.78