Question

4) Given 800,000 in current savings, and an expected remaining life expectancy of 15 years, inflation of 3%, and investment r of 8%,

a) what annuity due could be purchased?

b) what annuity due could be purchased leaving 200,000 behind in 15 years (current dollars, not inflation adjusted).

Answer 1

ANSWER DOWN BELOW. FEEL FREE TO ASK ANY DOUBTS. THUMBS UP PLEASE.

We are using BGN(BEGIN) mode on the calculator as it is an annuity due.

For that press 2nd + PMT

Then Press 2nd + Enter. You will be in BGN Mode.

a. Using Financial Calculator:

N = 15

I/Y = ((1.08/1.03)-1)*100% = 4.85437

PV = -800,000

FV= 0

CPT Press PMT = 72,783.80

Annuity due value per year = 72,783.80

b.

Using a Financial Calculator:

N = 15

I/Y = ((1.08/1.03)-1)*100% = 4.85437

PV = -800,000

FV= 200,000

CPT Press PMT = 63,847.11

Answer: Annuity due value per year =63,847.11

Alternative way:

Traditional way:

Formula: The present value of an annuity due (PV)

PV = {C× [1-(1+r)^-n]/r}×(1+r)}

PV = Present value (The cumulative amount available at Present).

C= Periodic cash flow.

r =effective interest rate for the period.

n = number of periods.

800,000= {C× [1-(1+4.85437%)^-15]/ 4.85437%}×(1+4.85437%)}

C = 72,783.80