Question

Consider a bank account starting with $1 (if $1 seems too small to you, you are welcome to multiple this and all other results by any desired amount, say, $1,000 or $100,000). If the bank gives you 100% interest rate (yes, I know, it’s not realistic, but just play along!), then after one year you have $2 in your account.

1) What will happen if instead the bank gives you 50% interest every half a year? How much money will you have in your account after 1 year?

2) How much money will you have after one year if the bank adds the interest of 25% every quarter? Did the amount increase/decrease/stay the same?

3) Create a table corresponding to compounding your dollar monthly, daily, hourly, and even every minute.

Answer 1

We are given with the following information in the above question:

The Principal Amount = $1

PART (1) Interest Rate = 50%

Time Period = 1 year

Compounded = Half Yearly

We have the following formula for calculating the Future Value when compounded half yearly:

where,

FV= FUTURE VALUE

P= PRINCIPAL

r= Rate of interest

t= Time period

This implies that

=$1.56

we will have $1.56 after 1 year.

PART (2) Interest rate= 25%

Time period= 1 year

Compounded= Quarterly

We have the following formula for calculating the Future Value when compounded quarterly:

where,

FV= FUTURE VALUE

P= PRINCIPAL

r= Rate of interest

t= Time period

This implies that,

=$1.27

If the bank adds the interest of 25% quarterly, the amount decreases.

PART (3) We take the rate of Interest to be 100% as given in the question.

The formula for compounding remains the same, except for 'r' and 't'

Principal	Monthly(r/12 , 12t)	Daily(r/365 , 365t)	Hourly(r/8760 , 8760t)	Minute(r/525600 , 525600t)
$1	$2.61	$2.68	$2.71	***

*** There was an error computing the amount since the numbers are very large.