Question

15) You are offered $1,100 after four years (Offer 1) or $250 a year for four years (Offer 2). If you can earn 5 percent on your funds, calculate the future values of both payments. Round your answers to the nearest dollar.

FV(Offer 1):? FV(Offer 2): ?

Which offer will you accept?

If you can earn 16 percent on your funds, calculate the future values of both payments. Round your answers to the nearest dollar. FV(Offer 1):? FV(Offer 2): ?

Which offer will you accept, if you can earn 16 percent on your funds? Why are your answers different? The choices are different as the higher interest rate .

16) This extended problem covers many of the features of a mortgage. You purchase a town house for $300,000. Since you are able to make a down payment of 10 percent ($30,000), you are able to obtain a $270,000 mortgage loan for 15 years at a 6 percent annual rate of interest.. Round your answers to the nearest dollar.

What are the annual payments that cover the interest and principal repayment?

How much of the first payment goes to cover the interest?

How much of the loan is paid off during the first year?

What is the interest payment during the second year?

What is the remaining balance after the second year?

Why did the interest payment change during the second year? The annual in the amount owed each subsequent interest payment.

17)You have an IRA worth $250,000 and want to start to make equal, annual withdrawals (i.e., distributions from the account) for 20 years. You anticipate earning 5 percent on the funds. (To facilitate the calculation, assume an annuity due.). Round your answers to the nearest dollar.

How much can you withdraw each year?

Since you are earning 5 percent on your investments, how much of the withdrawal consumes your investments?

How much will be in the account at the end of the first year?

How much do you earn on your investments in the account during the second year?

How much will be in the account at the end of the second year?

Answer 1

Q 15) i) Future value of the following offers:

a) Offer 1 : Future value = Amount*(1 + rate) ^years

Amount = $1100 , Rate = 5% or 0.05 , years = 4

Offer 1: Future value = $1100*(1 + 0.05)^4

Offer 1: Future value = $1100 * 1.2155 = $1337.05

b) Offer 2 : Future value = Annual amount *(((1 + i) ^n) - 1) / i)

Annual amount = $250 , i = 5% or 0.05, n = 4

Future value = $250 * (((1 + 0.05)^4) - 1) / 0.05)

Future value = $250 * (0.2155 / 0.05) = $250 * 4.31

Future value = $1077.50

Ans: Offer 1 should be accepted due to it's higher future value of $1337.05 against offer 2 of $1077.50

ii) If Interest rate = 16% then

a) Offer 1: Future value = Amount * (1 + rate)^n

Amount = $1100, rate = 16% or 0.16, n = 4

Offer 1: Future value = $1100 * (1 + 0.16)^4

Offer 1: Future value = $1100 * 1.8106 = $1991.66

b) Offer 2: Future value = Annual amount * (((1+r)^n) - 1) / i)

Annual amount = $500, r = 16% or 0.16, n = 4

Offer 2: Future value = $500 * (((1+0.16)^4) - 1) / 0.16) = $500 * (0.8106/0.16)

Offer 2: Future value = $500 * 5.0663 = $2533.15

Ans: Offer 2 should be accepted due to it's higher future value than offer 1.

Q 16) Interest and principal schedule:

Year	Opening balance	Interest @ 6% (Opening balance * 6%)	Principal (Annual payment - Interest)	Closing balance (Opening balance - Principal)
1	270000	16200	11600	258400
2	258400	15504	12296	246104
3	246104	14766.24	13033.76	233070.24

i) Annual payments = Loan / ((1 - (1+i)^-n) / i)

Annual payments =270000/((1-(1+0.06)^-15)/0.06)

Annual payments = 270000 /9.7123 = 27800

ii) 1st year interest = 16200

iii) 1st year loan repaid = 11600

iv) 2nd year interest = 15504

v) balance after 2nd year = 246104

vi) As interest calculated on the opening year loan balance due to which interest changed.