g. (Related to Checkpoint 6.1) (Loan amortization) On December 31, Beth Klemkosk

Question

g. (Related to Checkpoint 6.1) (Loan amortization) On December 31, Beth Klemkosky bought a yacht for $50,000. She paid $14,000 down and agreed to pay the balance in 13 equal annual installments that include both the principal and 15 percent interest on the declining balance. How big will the annual payments be?? a. On December 31, Beth Klemkosky bought a yacht for $50,000 and paid $14,000 down, how much does she need to borrow to purchase the yacht? s[] (Round to the nearest dollar.) b. If Beth agrees to pay the loan plus 15 percent compound interest on the unpaid balance over the next 13 years in 13 equal end-of-year payments, what will those equal payments be? (Related to Checkpoint 6.2) (Present value of annuity payments) The state lottery's million-dollar payout provides for $1.1 million to be paid in 25 installments of $44,000 per payment. The first $44,000 payment is made immediately, and the 24 remaining $44,000 payments occur at the end of each of the next 24 years. If 9 percent is the discount rate, what is the present value of this stream of cash flows? If 18 percent is the discount rate, what is the present value of the cash flows? a. If 9 percent is the discount rate, the present value of the annuity due is . (Round to the nearest cent) b. If 18 percent is the discount rate, the present value of the annuity due is []. (Round to the nearest cent.)

Explanation / Answer

8 a)She needs to Borrow 50000-14000=$36000 to pay for the yacht.

b) equal payments=(BorrowedAmt*r)/(1-1/(1+r)T) ,BorrowedAmt=36000 ,interest rate=15%=r,T=13

equal payments=(36000 *.15)/(1-1/(1.15)13) = 5400/0.83747 =$6447.98

9a) Let A be equal payments paid over T years ar rate of r%.

P=Present Value of stream of cash flows A/year  paid over T years ar rate of r%= Present value of all future pays of Annuities A obtained by discounting A at rate of interest r

P=A/(1+r)0+ A/(1+r)1+........+A/(1+r)T

P=A+A(1/(1+r)1+........+1/(1+r)T)

1/(1+r)1+........+1/(1+r)T GP with first term =1/(1+r) and common ratio=cr=1/(1+r) and no of terms=T

Sum of GP= first term*(1-crT)/(1-cr) = 1/(1+r) * (1-1/(1+r)T)/(1-1/(1+r))=(1-1/(1+r)T)/(r)

So P=A+(A/r)*(1-1/(1+r)T) put values A=44000,T=24 and

a) r=9%=.09

P=44000+(44000/.09)*(1-1/(1.09)24)

P=44000+427090.92=471090.92, thus the present value of annuity due is $471090.92

b)r=18%=.18

P=44000+(44000/.18)*(1-1/(1.18)24)

P=44000+239841.75=283841.75,thus the present value of annuity due is $283841.75

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