Question

Find the present values of these ordinary annuities. Discounting occurs once a year. Do not round intermediate calculations. Round your answers to the nearest cent.

a. $200 per year for 16 years at 16%.

b. $100 per year for 8 years at 8%.

c. $700 per year for 8 years at 0%.

d. Rework previous parts assuming they are annuities due.

Present value of $200 per year for 16 years at 16%: $  

Present value of $100 per year for 8 years at 8%: $  

Present value of $700 per year for 8 years at 0%: $  

Answer 1

a]

PV of annuity = P * [1 - (1 + r)^-n] / r,

where P = periodic payment. This is $200.

r = interest rate per period. This is 16%.

n = number of periods. This is 16.

PV of annuity = $200 * [1 - (1 + 16%)^-16] / 16%

PV of annuity = $1,133.70

b]

PV of annuity = P * [1 - (1 + r)^-n] / r,

where P = periodic payment. This is $100.

r = interest rate per period. This is 8%.

n = number of periods. This is 8.

PV of annuity = $100 * [1 - (1 + 8%)^-8] / 8%

PV of annuity = $574.66

c]

As the interest rate is 0%, there is no discounting required.

PV = $700 * 8 = $5,600

d]

a]

PV of annuity due = P + [P * [1 - (1 + r)^-(n-1)] / r]

where P = periodic payment. This is $200.

r = interest rate per period. This is 16%.

n = number of periods. This is 16.

PV of annuity = $200 + [$200 * [1 - (1 + 16%)^-(16-1)] / 16%]

PV of annuity = $1,315.09

b]

PV of annuity due = P + [P * [1 - (1 + r)^-(n-1)] / r]

where P = periodic payment. This is $100.

r = interest rate per period. This is 8%.

n = number of periods. This is 8.

PV of annuity = $100 + [$100 * [1 - (1 + 8%)^-(8-1)] / 8%]

PV of annuity = $620.64

c]

As the interest rate is 0%, there is no discounting required.

PV = $700 * 8 = $5,600