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Future Value: $0.00

Considering the current value, interest rate, and number of periods, the future value formula determines the investment’s value at a later time. FV = PV x (1+r)^n is the basic formula, in which n is the number of periods, r is the interest rate, and FV is the future value.$\text{FV} = \text{PV} \times (1 + r)^n$A more intricate formula is applied if the interest is compounded more frequently. A compounding frequency variable, k, is included. You can use a present value calculator and a compound annual growth rate calculator if you don’t have all the values.

The future investment value is calculated using the formula for compound interest. The formula takes into account the initial investment, the annual interest rate, the number of years the money is invested, and the number of times the interest is compounded per year.

The formula for calculating the future value ($FV$) is:

$FV=P(1+nr )_{nt}$

where:

- $P$ is the principal amount (initial investment).
- $r$ is the annual interest rate (decimal).
- $n$ is the number of times the interest is compounded per year.
- $t$ is the number of years.

Suppose you have an initial investment of $10,000, an annual interest rate of 5%, and you want to invest it for 10 years with the interest compounded monthly.

**Initial Investment (P):**$10,000**Annual Interest Rate (r):**5% or 0.05**Number of Years (t):**10**Compounding Periods per Year (n):**12 (monthly)

Plug these values into the formula:

$FV=10000(1+120.05 )_{×}$

Calculate step-by-step:

- Calculate the monthly interest rate:

$120.05 =0.004167$

- Add 1 to the monthly interest rate:

$1+0.004167=1.004167$

- Calculate the exponent (total number of compounding periods):

$12×10=120$

- Raise the base (1.004167) to the power of 120:

$1.00416_{120}≈1.647009$

- Multiply the principal by the result:

$10000×1.647009=16470.09$

So, the future value of the investment after 10 years, compounded monthly, would be approximately $16,470.09.