Suppose you deposit into a savings account one cent on January 1, three cents on January 2, nine cents on January 3, and so on, tripling the amount of your deposit each day (assume that you use an electronic bank that is open every day of the year). How much will you deposit on January 9?

Answer: the deposit on January 9 will be $6561

Step-by-step explanation:

Suppose you deposit

one cent on January 1,

three cents on January 2,

nine cents on January 3, and so on, since you are tripling the amount of your deposit each day, the amount of money each day is increasing in geometric progression.

The formula for the nth term, Tn of a geometric progression is

Tn = ar^n-1

Where

a is the first term of the sequence

n is the number of terms of the sequence

r is the common ratio

From the information given

a = 1 (amount deposited on January 1)

r = 3 (the rate at which the amount is increasing)

n = 9 (9 days from January 1 to January 9)

T9 = amount on January 9.

It becomes

T9 = 1 * 3^ (9-1) = 3^8

T9 = $6561

9th January = 6561 cent = 65.61 dollars

Step-by-step explanation:

so on tripling the amount, one by one and multiplying each amount by 3, you will get the next day amount

ist January = 1 cent

2nd January = 3 cent

3rd January = 9 cent

4th January = 27 cent

5th January = 81 cent

6th January = 243 cent = 2.43 dollar

7th January = 729 cent = 7.29 dollars

8th January = 2187 cent = 21.87 dollars

9th January = 6561 cent = 65.61 dollars