Question

all of three please

LOANS: Written Answer Questions (3) Due 7/2 1 Sylvia is repaying a loan of X by making 17 annual payments of 100. Each payment consists of interest on the loan at 5% effective and an amount that is deposited in a sinking fund earning 4% effective. At the end of 17 years, the amount in the sinking fund is equal to the original loan amount accumulated with interest at the sinking fund rate. Determine X. 2. Henry is repaying a loan at an effective rate of 5% a year. The payments at the end of each year for 10 years are 1000 each. In addition to the loan payments. Henry pays premiums for loan insurance at the beginning of each year. The first premium is 0.5% of the original loan balance, the second premium is 0.5% of the loan balance immediately after the first loan payment, etc., and the tenth premium is 0.5% of the loan balance immediately after the 9th loan payment. The present value of the premiums at 5% is X. Determine X. 3. A house is purchased for $200,000 and a 20% down payment is made. The balance is financed by a 30 year adjustable rate mortgage with monthly payments. The initial interest rate is 12% per annum, compounded monthly. Just after the 240th payment, the interest rate is increased to 14% compounded monthly. The payments remain at the original amount until a final smaller payment fully repays the loan. What is the total number of monthly mortgage payments made over the life of the loan, including the final smaller payment?

Answer 1

Loan amount=X

Effective interest rate=5%

Number of payments=17

Annual Payment=100

Annual interest at 5%=X*0.05

Principal deposited in sinking fund each year=100-0.05X

Compound Amount Factor(CAF)=(F/A,i,N)=(((1+i)^N)-1)/i

i= Interest rate in sinking fund =4%=0.04

N=Number of Years=17

Compound Amount Factor(CAF)=(F/A,4%,17)=(((1+0.04)^17)-1)/0.04=23.69751

Loan Balance at end of 17 Years=X

Sinking fund accumulated at sinking fund rate=23.69751*(100-0.05X)

23.69751*(100-0.05X)=X

2369.751-1.184876X=X

X*(1+1.184876)=2369.751

X=2369.751/2.184876=1084.616

X=1085 (Rounded to whole number)