Question

Colin has an inheritance that promises to pay him 7 year-end amounts of $5,000 starting exactly 2 years and 3 months from today. If he earns 4.4% p.a., how much is the inheritance worth in present-day dollars? Select one: a. $27,151.62 b. $28,022.03 c. $26,841.03 d. $25,558.17

Answer 1

Sol:

PMT = $5000

Interest rate (r) = 4.4% p.a

Period (n) = 7 years

First we have to calculate the PV a year before first annuity payment

Present value (PV) = PMT x (1-(1+r)^-n/r

PV = 5000 x (1-(1+4.4%)^-7/4.4%

PV = 5000 x (1-1.044)^-7/0.044

PV = 5000 x 5.9143 = $29,571.63

Now we have to calculate the PV at year 0 (1 year and 3 months later)

FV = $29,571.63

Period (n) = 1.25

PV = FV / (1+r)^n

PV = $29,571.63 / (1+4.4%)^1.25

PV = $29,571.63 / (1.044^1.25)

PV = $28,022.03

Therefore inheritance worth in present-day dollars is $28,022.03

Answer is b. $28,022.03