You have been working really hard for the last few months and have saved $2000. You decide that you want to put your money in a high-yield savings account in order to gain the most amount of money possible. In five years, you want to take out the money and use it as a down payment on a car. The bank you have chosen to use is experimenting with a “Choose Your Own Savings Account” plan that allows you to set some of the term options for your own account. Your task is to determine the best possible options for your account so you end up with the most money possible in five years. Important letters and words to know:

P: Principal (The amount initially invested. In this case, you are investing $2000)
A: Final Amount (The final amount in the account after t years)
t: Time (In this case, if t is the number of years, t = 5)
r: Rate (Rate will always be given as a percentage, so you need to convert it to a decimal)
n: Number of Times Compounded (If your interest is compounded quarterly, it is compounded 4 times per year, etc.)
e: Euler’s Constant (a number discovered by a mathematician named Euler (pronounced 'oi-ler'). This value for e is about 2.71828, but most calculators have an e button)

Option 1: Simple Interest

The first option the bank offers you is indeed the simplest. Simple Interest does not include any exponents or fractions, so it has to be the best, right? Search online for the formula for simple interest:

Simple interest formula:

In this case, the rate they offer you is 1.5%. Calculate the Final Amount in your account based
on this offer.

Final amount:
Option 2: Interest Compounded Yearly

This is the first option with compound interest. Compound interest means that a specific rate is applied as interest a specific amount of times per year. Here is the formula for compound interest:
A = P(1 + rn)nt
In this case, the rate they offer you is 1.5%, and the interest is compounded yearly (n = 1). Calculate the Final Amount in your account based on this offer.

Final amount:

Option 3: Interest Compounded Monthly

In this case, the rate they offer you is 1.5%, and the interest is compounded monthly (n = 12).
Calculate the Final Amount in your account based on this offer.

Final amount:

Option 4: Interest Compounded Daily

In this case, the rate they offer you is 1.5%, and the interest is compounded daily (n = 365).
Calculate the Final Amount in your account based on this offer.

Final amount:

Option 5: Continuous Compound Interest

In this case, the rate they offer you is 1.5%, and the interest is compounded continuously. Here is the formula for continuous compound interest:

A =Pert

Calculate the Final Amount in your account based on this offer.

Final amount:
Conclusion:

Which option is the best offer?

Is it significantly better than the other options? Why or why not?

Is putting money into a savings account only once a really productive idea? Why or why not?

What are some ways to improve the plan to save for a down payment?