The accumulated value of an investment is the original amount plus interest earned. An earned value formula can determine the total amount of cash flow in each payment. This concept is important for annuity payments and understanding the time value theory of money.
The accumulated value of an investment is equal to the amount originally invested plus any interest that accrues over the life of the investment. This value is often used in discussions of annuities, which are investments, like bonds, that pay some type of regular payment to an investor. Finding the accumulated value requires knowing the interest rate of the investment, the number of times that interest will be compounded, and the original amount of the investment. A formula for this value shows the investor how much his investment is worth at the present time, even though the actual payments will not be made until well into the future.
Investors often rely on so-called fixed income as part of their portfolios. Fixed income basically means that investors will receive periodic payments at certain times, usually at some rate if interest rate is included. This can work both ways, as people often make regular payments to pay off loans to buy big-ticket items like houses or cars. In either case, the full value of the payment, known as the earned value, represents the amount the lender in the transaction may receive upon completion of the transaction.
For example, imagine someone buying a bond with a face value of $5,000 US dollars (USD) that pays an annual interest rate of two percent for a term of five years. That means the investor will receive $1,000 in principal at the end of each year. In addition, they will also receive the interest rate, which, when compounded, will result in a higher payment each year. The accumulated value would add up to $5,000 USD plus all interest payments.
There is a formula to determine earned value. To calculate it, start by taking the interest rate plus one and raising it to the power equal to the number of annuity payments. Then subtract one from that number and divide the difference by the interest rate. Finally, that multiplies the total by the amount of cash flow in each payment. In the example above, the interest rate is 0.02, the number of payments is five, and the cash flow per period is $1,000. Plugging all those numbers into the earned value formula gives a total of $5,204.04 USD.
In that example, the accumulated value shows the investor what to expect from their original investment. It is an example of the time value theory of money, which is an important concept with annuity payments. Understanding this concept can help investors realize whether an investment will pay off compared to inflation values that decrease the value of money over time.
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