Future Value, Single Amount

Multi-period investments occur over more than one period (usually multiple years) and can accrue simple or compound interest.

If the time frame is longer than one period, there are two primary ways of determining how much an investment will be worth in the future.

The first concept of accruing (or earning) interest is called "simple interest." Simple interest means that you earn interest only on the principal. Your total balance will go up each period because you earn interest each period, but the interest is paid only on the amount you originally borrowed/deposited. Simple interest is expressed through the formula in.

\(FV = PV \cdot (1+rt)\)

Simple Interest Formula Simple interest is when interest is only paid on the amount you originally invested (the principal). You don't earn interest on interest you previously earned.

Suppose you deposit $100 in the bank and earn 5% annual interest. After one year, you earn 5% interest, or five, bringing your total balance to 105. One more year passes, and it's time to accrue more interest. Since simple interest is paid only on your principal ($100), you earn 5% of $100, not 5% of 105. That means you earn another five in the second year and will earn $5 for every year of the investment. In simple interest, you earn interest based on the original deposit amount, not the account balance.

The second way of accruing interest is called "compound interest." In this case, interest is paid at the end of each period based on the balance in the account. In simple interest, only how much the principal is that matters. In compound interest, the balance matters.

Compound interest is named as such because the interest compounds: Interest is paid on interest. The formula for compound interest is.

\(FV = PV \cdot (1+i)^t\)

Compound Interest Interest is paid at the total amount in the account, which may include interest earned in previous periods.

Suppose you make the same $100 deposit into a bank account that pays 5%, but this time, the interest is compounded. After the first year, you will again have $105. At the end of the second year, you also earn 5%, but it is 5% of your balance, or 105. You earn 5.25 in interest in the second year, bringing your balance to $110.25. In the third year, you earn interest of 5% of your balance, or $110.25. You earn 5.51 in interest, which brings your total to 115.76.

Compare compound interest to simple interest. Simple interest earns you 5% of your principal yearly or five a year. Your balance will go up linearly each year. Compound interest earns you 5 in the first year, $5.25 in the second, a little more in the third, and so on. Your balance will go up exponentially.

Simple interest is rarely used compared to compound interest, but it's good to know both types.