Question

Your crazy uncle left you a trust that will pay you $16,000 per year for the next 23 years with the first payment received one year from today. If the appropriate interest rate is 4.9 percent, what is the value of the payments today

Answer 1

Step-by-step explanation:

To calculate the present value of the future payments, we can use the formula for the present value of an annuity:

PV = PMT × (1 - (1 + r)^(-n)) / r

Where:

PV = Present value

PMT = Payment per period

r = Interest rate per period

n = Number of periods

In this case:

PMT = $16,000 per year

r = 4.9% = 0.049 (decimal)

n = 23 years

Let's calculate the present value:

PV = $16,000 × (1 - (1 + 0.049)^(-23) / 0.049

PV ≈ $16,000 × (1 - 0.66721) / 0.049

PV ≈ $16,000 × 0.33279 / 0.049

PV ≈ $108,666.12

Answer 2

$217,866.12

Step-by-step explanation:

Using the annuity payment formula

P = r(PV)/[1 - (1 + r)^ -n]

Where

r is rate per period = 49% = 0.049

PV is present value = ?

P is the payment = $16000

n is the number of periods = 1

Therefore

$16000 = 0.049PV / (1 − 1.0490)^-1

= 0.049PV = $16000 × (1 - 1/1.049)

Make PV the subject

PV = $16,000 × [(1 −1/1.049)/0.049]

= $217,866.12