Explain why the amount of money in the account at the end of t years is given by the formula:

P = P0 (1 + r/n) ^nt

See below.

Step-by-step explanation:

This is the formula for the value of an investment with compound interest.

PO is the initial amount invested, P is the amount after investing t years, r is yearly rate of interest (as a fraction) and n is the number of times interest is paid per year.

An example using values will serve to explain it further. If the rate is 2% (which = 0.02) per year and the interest is added to the account every 6 months (twice a year) then, in the parentheses we have (1 + 0.02/2). The 1 is there because we are talking about the amount of money PLUS the interest. Now if we are dealing with 5 year's investment, the exponent nt will be 2*5 = 10 because the interest is paid 2 times a year over 5 years: - 10 payments. So if we invest 10,000 at 2% interest over 5 years with 2 interest payments a year the total after 5 years = P = 10,000 (1 + 0.02/2) ^10 = 11,046.22.