Final answer:
The formula P = P * (1+1/n)^a refers to compound interest, where interest is earned on the initial deposit as well as on the accumulated interest from previous periods. This leads to exponential growth of the initial investment, which is dramatically more than what simple interest would yield over the same period.
Step-by-step explanation:
The amount of money in an account at the end of the first year is given by a formula with a raised exponent due to the concept of compound interest. Compound interest is the addition of interest to the principal sum of a deposit, where the interest that has been added also earns interest. This leads to the compound growth of the investment.
When a financial saving grows at a certain interest rate over time, the formula can be represented as PV(1+i)^n = FV, where PV is the present value, FV is the future value, i is the interest rate, and n is the number of compounding periods. For instance, with a simple interest, a $100 deposit at an interest rate of 5% held for one year would give you $5 in interest. However, with compound interest, that interest would also earn interest over time.
The formula P = P * (1+1/n)^a expresses the amount after a year with annual compounding; 'P' is the principal, 'a' is the number of years, and 'n' is the number of compounding periods per year. Applying this formula, you calculate the growth of your investment at the end of each compounding period, including the interest that has been accumulated so far.