Michael opened a savings account with an initial deposit of $100. Each year, his account earned interest at a rate of 8% of the balance in the previous year.

Question

Let h(n) represent Michael's account balance at the nth year of saving.
a. Is it arithmetic or geometric?
b. Write in explicit formula.

Answer 1

a. This is a geometric sequence because the amount in the account earns interest at a fixed rate each year based on the previous year's balance.

b. The explicit formula for the amount in Michael's savings account at the nth year can be written as:
h(n) = 100(1.08)^n
where 100 represents the initial deposit, 1.08 represents the growth factor (1 + 8% expressed as a decimal), and n represents the number of years.