Final answer:
The question deals with calculating the future value of investments using compound interest for a lump sum and an annuity. It involves applying specific finance formulas to determine the value of these investments over time. Examples include single lump sum investments and calculating simple interest.
Step-by-step explanation:
The question involves the application of finance formulas related to the future value of lump sums and annuities in a compound interest context. Using the formulas provided, a student can calculate the future size of an investment (S) given a principal amount, an interest rate, and a period. The principal (P) represents the initial amount, the rate (r) is the annual interest rate, and the time (t) represents the number of years the money is invested or borrowed for.
For example, to find the future value of a single lump sum using compound interest, the formula P(1 + r)^t is used. This can be seen in the provided reference where $1,000 at a 2% annual interest rate compounded over 5 years results in $1,104.08. Similarly, for an annuity (a series of equal payments), the formula S = P[(1+r)^t - 1] / r is used to find the future value of the regular payments.
To practice calculating simple interest, one would multiply the original principal by the rate of interest and the time the interest is applied using the formula Interest = Principal × rate × time. An example provided is depositing $100 at a 5% rate for one year, which yields $5 in interest. This is a fundamental financial concept that's helpful in understanding more complex ideas.