Question
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?
Answers
GPT-4o mini
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.
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.