You know that money in an account where interest is compounded semi-annually

will earn interest faster than money in an account where interest is compounded

annually. You wonders how much interest can be earned by compounding it more and

more often. In this problem we investigate his question.

For ease of computation, let’s suppose a man invests $1 at a 100% interest rate. If his

interest is compounded annually, his year-end balance will be:

If his interest is compounded semi-annually, he earns half the annual interest at mid-

year, and so his mid-year balance is:

At year-end he earns the other half of his annual interest giving him a year-end balance

of:

(because we see above $1.5 = $1.5(1+ ) we can use substitution)

1

2

a. You are making an initial deposit of $1000 in an account that yields 5% interest

annually. Following the pattern given above, find your year-end balance. (Show

calculations and round to the nearest penny) 10 pts

balanceby following the pattern is;$1050.## What is the year-end balance of the account following the pattern in which case, the interest rate is 5%?

5%.$1,000.$1,050.interest rate;