Question

Peter has an inheritance that promises to pay him 11 year-end amounts of $5,000 starting exactly 3 years and 3 months from today. If he earns 4.2% p.a., how much is the inheritance worth in present-day dollars?

Select one:

a. $37,910.15

b. $39,502.38

c. $42,258.17

d. $41,154.33

Answer 1

The correct option is a. $37,910.15

The present value is computed as shown below:

Present value = Annual payment x [ (1 - 1 / (1 + r)n) / r ]

= $ 5,000 x [ (1 - 1 / (1 + 0.042)^11)/0.042]

= $ 5,000 x 8.666737247

= $ 43333.686235

The above computed value is of 3 years and 3 months.

So, the present value will be as follows:

= $ 43333.686235/1.042^3.25=37910.153925692

= $ 37910.15 (Approx.)

Explanation:

Present value of annuity 3 years and 3 months from today;

=PVA=A*[(1-1/(1+r)^n))]/r

Where,

PVA= is present value of annuity

A =is annual payment

r= is interest rate

n= is number of years

Therefore PVA starting 3 years and 3 months from today

=5000 x [ (1 - 1 / (1 + 0.042)^11)/0.042]

= 5000*8.666737

= $43333.685

Present value today of the lump sum amount of $43333.685 is calculated below

Present Value = Future Value/(1+r)n

PV = $43333.685/(1+0.042)^(3+3/12)

PV = $43333.685/(1.042)^3.25

PV = $43333.685/1.143062788

= $37910.15

Hence, the correct answer is option is a. $37,910.15