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The accumulated value of an investment is equal to the amount originally invested plus any interest that will accrue over the life of the investment. This value is often used in discussions about annuities, which are investments, like bonds, that pay in some sort of regular payments to an investor. Finding the accumulated value requires knowing the rate of interest of the investment, the amount of times that interest will be compounded, and the original amount of the investment. A formula for this value shows an investor how much his investment is worth at the current time even though the actual payouts won't be realized until well in the future.
Investors often rely on so-called fixed income as a part of their portfolios. Fixed income basically means that the investors will receive periodic payouts at certain times, usually with some sort if interest rate included. This can work both ways, since people often make regular payments to pay off loans to buy high-priced items like houses or cars. In any case, the total value of the payout, known as the accumulated value, represents the amount that the lender in the transaction stands to receive at the completion of the transaction.
For an example, imagine someone who buys a bond with a face value of $5000 US Dollars (USD) that pays off a yearly interest rate of two percent for a term of five years. That means that the investor will be receiving $1000 USD in principal at the end of each year. In addition they will also be receiving the interest rate, which, by compounding, will yield a higher payout each year. The accumulated value would add up to $5,000 USD plus all of the interest payments.
There is a formula for determining accumulated value. To calculate it, begin by taking the interest rate plus one and raising that to the power equal to the number of payments on the annuity. Then subtract one from that number, and divide the difference by the interest rate. Finally, that multiply the total by the amount of cash flow in each payment. In the above example, the interest rate is .02, the number of payments is five, and the cash flow per period is $1,000 USD. Plugging all of those numbers into the accumulated value formula yields a total of $5204.04 USD.
In that example, the accumulated value shows the investor what to expect from his original investment. It is an example of the theory of the time value of money, which is an important concept with annuity payments. Understanding this concept can help investors realize if an investment will be worthwhile when compared to inflation values that lower the value of money over time.