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

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


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


  1. By virtue of the pattern above, it follows that the year-end balance by 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%?

    It follows from the task content that the interest rate of the account arrangement is; 5%.
    On this note, it follows that if the initial deposit in the account is; $1,000.
    We can determine the year-end balance as follows;
    Year-end balance = $1000(1.05)
    = $1,050.
    Read more on interest rate;


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