Suppose you deposit $1,714.00 into and account 5.00 years from today into an account that earns 11.00%. How much will the account be worth 11.00 years from today?

1 answer

To determine the future value of the account after 11 years, we first need to calculate how much interest will be earned on the deposit of $1,714 over the time period prior to the investment maturing.

You will deposit the money today, and it will earn interest for a total of \( 11 \) years. However, since the deposit is made \( 5 \) years from today, the money will earn interest for \( 11 - 5 = 6 \) years from the time of deposit.

We'll use the formula for future value (FV) of a single sum:

\[ FV = PV \times (1 + r)^n \]

Where:

  • \( FV \) = future value
  • \( PV \) = present value (the initial deposit)
  • \( r \) = annual interest rate (as a decimal)
  • \( n \) = number of years the money is invested

In this case:

  • \( PV = 1714 \)
  • \( r = 11% = 0.11 \)
  • \( n = 6 \)

Now plug in the values:

\[ FV = 1714 \times (1 + 0.11)^6 \]

Calculating:

\[ FV = 1714 \times (1.11)^6 \]

Calculating \( (1.11)^6 \):

\[ (1.11)^6 \approx 1. we have \( (1.11)^6 \approx 1.771561 \)

Now substituting back into the equation:

[ FV \approx 1714 \times 1.771561 \approx 3032.170274 \]

Rounding to two decimal places:

\[ FV \approx 3032.17 \]

Therefore, the account will be worth approximately $3,032.17 11 years from today.