Question

Your grandmother would like to share some of her fortune with you. She offers to give you money under one of the following scenarios (you get to choose): 1. $8,750 a year at the end of each of the next seven years 2. $48,750 (lump sum) now 3. $99,350 (lump sum) seven years from now Calculate the present value of each scenario using a 6% interest rate. Which scenario yields the highest present value

Answer 1

The most profitable option is the third one.

Step-by-step explanation:

Escenario 1:

$8,750 a year at the end of each of the next seven years

First, we need to calculate the future value using the following formula:

FV= {A*[(1+i)^n-1]}/i

A= annual payment

FV= {8,750*[(1.06^7) - 1]} / 0.06

FV= $73,446.08

Now, the present value:

PV= FV / (1 + i)^n

PV= 73,446.08 / 1.06^7

PV= $48,845.78

Escenario 2:

Lump-sum= $48,750

Escenario 3:

$99,350 (lump sum) seven years from now

PV= 99,350 / 1.06^7

PV= $66,073.42

The most profitable option is the third one.