Question

What is the value today of a money machine that will pay $1,598.00 per year for 22.00 years? Assume the first payment is made 2.00 years from today and the interest rate is 12.00%.

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#2

What is the value today of a money machine that will pay $2,393.00 every six months for 18.00 years? Assume the first payment is made six months from today and the interest rate is 11.00%.

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#3

What is the value today of a money machine that will pay $1,732.00 every six months for 12.00 years? Assume the first payment is made 5.00 years from today and the interest rate is 9.00%.

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#4

What is the value today of a money machine that will pay $6,682.00 per year for 24.00 years? Assume the first payment is made today and that there are 24.0 total payments. The interest rate is 12.00%.

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#5

Derek will deposit $4,345.00 per year for 14.00 years into an account that earns 7.00%. The first deposit is made next year. How much will be in the account 14.0 years from today?

Answer 1

Answer to Question 1:

Annual payment = $1,598
Period = 22 years
Interest rate = 12%

First payment is made 2 years from today

Present value = $1,598/1.12^2 + $1,598/1.12^3 + … + $1,598/1.12^22 + $1,598/1.12^23
Present value = $1,598 * (1/1.12) * (1 - (1/1.12)^22) / 0.12
Present value = $1,598 * 6.825577
Present value = $10,907.27

Answer to Question 2:

Semiannual payment = $2,393
Semiannual Period = 36 (18 years)
Annual interest rate = 11%
Semiannual interest rate = 5.50%

Present value = $2,393/1.055 + $2,393/1.055^2 + … + $2,393/1.055^35 + $2,393/1.055^36
Present value = $2,393 * (1 - (1/1.055)^36) / 0.055
Present value = $2,393 * 15.536068
Present value = $37,177.81