Question

You need to have $25,956 avallable at the end of 10 years. How much to do you have invest each year, starting at the end of this year, for 10 years to achieve this goal if the interest rate is 76?

Answer 1

To calculate the annual investment required to accumulate $25,956 at the end of 10 years with an interest rate of 76%, we can use the formula for the future value of an ordinary annuity:

\[FV = P \times \left(1 + r\right)^n - 1\]

Where:

FV = Future value (target amount)

P = Annual investment

r = Interest rate

n = Number of years

Plugging in the given values, we have:

\[25,956 = P \times \left(1 + \frac{76}{100}\right)^{10} - 1\]

Simplifying the equation:

\[1.76^{10}P = 25,956 + 1\]

\[P = \frac{25,957}{1.76^{10}}\]

Using a calculator, we find that \(1.76^{10} \approx 13.365\). Now we can calculate the annual investment:

\[P \approx \frac{25,957}{13.365}\]

\[P \approx 1,943.13\]

Therefore, you would need to invest approximately $1,943.13 each year, starting at the end of this year, for 10 years at an interest rate of 76% to accumulate $25,956 at the end of the 10-year period.