Question

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

Answer 1

Answer:

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.