Question

Please ANSWER ALL (explanation with or without BA 2 calculator greatly appreciated)

#1.

What is the value today of a money machine that will pay $3,042.00 every six months for 11.00 years? Assume the first payment is made 5.00 years from today and the interest rate is 6.00%

#2.

What is the value today of a money machine that will pay $4,796.00 per year for 8.00 years? Assume the first payment is made today and that there are 8.0 total payments. The interest rate is 4.00%.

#3

Derek will deposit $1,188.00 per year for 10.00 years into an account that earns 7.00%. The first deposit is made next year. How much will be in the account 10.0 years from today?

#4

Derek will deposit $6,869.00 per year for 24.00 years into an account that earns 18.00%, The first deposit is made next year. How much will be in the account 37.00 years from today?

#5

Derek will deposit $2,229.00 per year for 16.00 years into an account that earns 5.00%. The first deposit is made today. How much will be in the account 16.0 years from today? Note that he makes 16.0 total deposits.

Answer 1

1)

Money machine will pay $3,042.00 every six months for 11.00 years

Interest rate = 6%

Semi annual interest rate = 6% / 2 =3%

No of periods = 11 years * 2 = 22 semi annual periods

First payment expected 5 years from today so we 'll have to tale the present value 4 year from day

Using the PVIFA formula to value these payments.

Value of Money machine payments 4 years from today = ((1 - (1 + semi annual interest rate)^{- no of periods}) / Semi annual interest rate) * Payment per 6 months

Value of Money machine payments 4 years from today = ((1 - (1 + 3%)^{- 22}) / 3%) * $3,042

Value of Money machine payments 4 years from today = $48,480.10

Discounting this amount for 4 years to get the present value of the amount today

Value of the Money machine payments today = Value of payments 4 years from today / (1 + interest rate)^{no of periods}

Value of the Money machine payments today = $48,480.10 / (1 + 6%)⁴

Value of Money machine payments today = $38,400.78

2) money machine will pay $4,796.00 per year for 8.00 years

interest rate = 4%

No of periods = 8 years

Using the PVIFA formula to value these payments.

Value of Money machine payments today = ((1 - (1 + interest rate)^{- no of periods}) / interest rate) * Payment per 6 months

Value of Money machine payments today = ((1 - (1 + 4%)^{- 8}) / 4%) * $4,796

Value of Money machine payments today = $32,290.24

3) Deposit  $1,188 per year for 10 years, starting next year

interest rate = 7%

Using the FVIFA formula to value these deposits

Value of these deposits in 10 years = (((1 + interest rate)^{no of periods} - 1) / interest rate) * Deposit per year

Since the deposit will be made 1 year from today the no of periods = 9 years

Value of these deposits in 10 years = (((1 + 7%)⁹ -1) / 7%) * $1,118

Value of these deposits in 10 years = $14,229.85

4) Deposit $6,869 per year for 24 years, starting next year

interest rate = 18%

Using the FVIFA formula to value these deposits

Value of these deposits in 24 years = (((1 + interest rate)^{no of periods} - 1) / interest rate) * Deposit per year

Since the deposit will be made 1 year from today the no of periods = 23 years

Value of these deposits in 24 years = (((1 + 18%)²³ -1) / 18%) * $6,869

Value of these deposits in 24 years = $1,679,380.15

Value of these deposits in 37 years = Value of these deposits in 24 years * (1 + interest rate)^{no of periods}

Value of these deposits in 37 years = $1,679,380.15 * (1 + 18%)¹³

Value of these deposits in 37 years = $14,441,593.32

5)  $2,229 per year for 16 years, first deposit made today

interest rate = 5%

Using the FVIFA formula to value these deposits

Value of these deposits in 16 years = (((1 + interest rate)^{no of periods} - 1) / interest rate) * Deposit per year

Since the deposit will be made today, the no of periods = 16 years

Value of these deposits in 16 years = (((1 + 5%)¹⁶ -1) / 5%) * $2,229

Value of these deposits in 16 years = $52,732.55