Question

Sutton deposited

$
7500
into an account paying
6.24
%
annual interest compounded monthly. How much money will be in the account after
7
years? (also called Future value).

Answer 1

Step-by-step explanation:

Answer 2

The future value (FV) of Sutton's deposit of $7500 into an account with a 6.24% annual interest rate compounded monthly after 7 years is approximately $11,407.88.

Step-by-step explanation:

To calculate the future value, we use the compound interest formula:

`\[FV = P \left(1 + (r)/(n)\right)^(nt)\]`

Where:

• FV is the future value of the investment/loan.
• P is the principal amount (initial deposit or loan amount).
• r is the annual interest rate (as a decimal).
• n is the number of times that interest is compounded per unit
  `\(t\).`
• t is the time the money is invested or borrowed for in years.

In this case:

`\(P = $7500\)`

`\(r = 6.24\% = 0.0624\) (converted to decimal)`

`\(n = 12\)` (compounded monthly)

`\(t = 7\)` years

Substitute these values into the formula:

`\[FV = 7500 \left(1 + (0.0624)/(12)\right)^((12 * 7))\]`

Calculate the expression:

`\[FV \approx 7500 \left(1 + 0.0052\right)^(84)\]`

`\[FV \approx 7500 * 1.5017962\]`

`\[FV \approx 11,407.88\]`

Therefore, after 7 years, Sutton's deposit will grow to approximately $11,407.88. This calculation takes into account the compounded interest, resulting in the final future value of the deposit.