Question

Your grandmother has given you a gift of $1500 for your birthday. You are thinking about your future and

considering two different options on how to manage your money. Option A: You take all of your $1500 and
deposit it into a savings account that has a 5% interest rate per year. Option B: You spend $500 on a new
Apple Watch and deposit the remaining $1000 in a savings account that has a 5.5% interest rate per year.
.
Which account would have the most in 10 years? 20 years? Mathematically, explain your reasoning.
Which option would you choose and why?
.

Answer 1

B

Explanation:

if you put the rest of your money in a savings account you can use that money for your college fund or maybe buy a car ect.

Answer 2

OPTION A yields the most money at 10 and 20 years. Hence Option A is the better choice for "thinking about your future"

Explanation:

In the absence of any more information, I am going to assume that Simple Interest applies. (see attached)

hence the applicable formula is:

A = P(1+rt), where

A = final amount after t years

P = Principal (beginning) amount ($1500 for option A and $1000 for option B)

r = annual interest rate (5% = 0.05 for option A and 5.5% = 0.055 for option B)

t = time (we are asked to evaluate t = 10 years and t = 20 years)

For option A :

P = $1500 and r = 5% = 0.05

A = P(1+rt)

A = 1500 [ 1 + (0.05)t]

at 10 years: A = 1500 [ 1 + (0.05)(10)] = $2,250

at 20 years: A = 1500 [ 1 + (0.05)(20)] =$3,000

For option B :

P = $1000 and r = 5.5% = 0.055

A = P(1+rt)

A = 1000 [ 1 + (0.055)t]

at 10 years: A = 1000 [ 1 + (0.055)(10)] = $1,550

at 20 years: A = 1000 [ 1 + (0.055)(20)] = $2,100

Comparing all the 4 results above, we can see that OPTION A yields the most money at 10 and 20 years. Hence Option A is the better choice for long term returns.