1 The Johnsons have accumulated a nest egg of 50000 that the

1. The Johnsons have accumulated a nest egg of $50,000 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 $2900/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 $3500. If local mortgage rates are 2.5%/year compounded monthly for a conventional 30-year mortgage, what is the price range of houses that they should consider? (Round your answers to the nearest cent.)

2. Find the periodic payment R required to amortize a loan of P dollars over t years with interest charged at the rate of r%/year compounded m times a year. (Round your answer to the nearest cent.)

P = 40,000, r = 2, t = 15, m = 4

3.The price of a new car is $32,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 8%/year compounded monthly. (Round your answers to the nearest cent.)

(a) What monthly payment will she be required to make if the car is financed over a period of 36 months? Over a period of 60 months?

(b) What will the interest charges be if she elects the 36-month plan? The 60-month plan?

60-month plan   

4. A group of private investors purchased a condominium complex for $2 million. They made an initial down payment of 12% and obtained financing for the balance. If the loan is to be amortized over 11 years at an interest rate of 8.6%/year compounded quarterly, find the required quarterly payment. (Round your answer to the nearest cent.)
$

Solution

1) we have EMI = P*R*(1+R)^N/[(1+R)^N-1]

Now R = 0.025/12

for monthly installment of 2900 we can take a loan of

P = EMI *[(1+R)^N-1]/[R*(1+R)^N]

P = 2900 *[(1+0.025/12)^360-1]/[0.025/12*(1+0.025/12)^360]

P = $733952.57

So with 50000 downpayment, they can purchase a house of $783952.57

Now for 3500 emi

P = 3500 *[(1+0.025/12)^360-1]/[0.025/12*(1+0.025/12)^360]

P = $ 885804.83

So they can purchase a house of 935804.83 with 50000 downpayment.

2) EMI (R)= P*(r/m)*(1+r/m)^t*m/[(1+r/m)^t*m-1]

P = 40,000, r = 2%,t = 15, m = 4;

R = 40000*(0.02/4)*(1+0.02/4)^15*4/[(1+0.02/4)^15*4-1]

R = $260.4 per month

3) total amount of car 32000, downpayment 8000;

24000 on loan at 8% interest

36 MONTH

EMI = 24000*(0.08/12)*((1+0.08/12)^36)/((1+0.08/12)^36-1)

EMI = $752

60 MONTH

EMI = 24000*(0.08/12)*((1+0.08/12)^60)/((1+0.08/12)^60-1)

EMI = $486.63

TOTAL MONEY PAID FOR 36MONTH PLAN

752*36=27072

interest = 27072-24000=3072

TOTAL MONEY PAID FOR 60MONTH PLAN

486.83*60=29210

interest = 29210-24000=5210

4) $2Million at 12% downpayment

so loan is at 1.76 million

8.6% quarterly.

EMI = 1760000*(0.086/4)*((1+0.086/4)^44)/((1+0.086/4)^44-1)

EMI = $ 62257.70